- published: 21 Mar 2022
- views: 1074
-
remove the playlistCage (graph Theory)
- remove the playlistCage (graph Theory)
Cage (graph theory)
In the mathematical area of graph theory, a cage is a regular graph that has as few vertices as possible for its girth.
Formally, an (r,g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. It is known that an (r,g)-graph exists for any combination of r ≥ 2 and g ≥ 3. An (r,g)-cage is an (r,g)-graph with the fewest possible number of vertices, among all (r,g)-graphs.
If a Moore graph exists with degree r and girth g, it must be a cage. Moreover, the bounds on the sizes of Moore graphs generalize to cages: any cage with odd girth g must have at least
vertices, and any cage with even girth g must have at least
vertices. Any (r,g)-graph with exactly this many vertices is by definition a Moore graph and therefore automatically a cage.
There may exist multiple cages for a given combination of r and g. For instance there are three nonisomorphic (3,10)-cages, each with 70 vertices : the Balaban 10-cage, the Harries graph and the Harries–Wong graph. But there is only one (3,11)-cage : the Balaban 11-cage (with 112 vertices).
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Cage_(graph_theory)
Cage9
HIDDEN ERROR: Usage of "current city" is not recognized
Cage9 is a Panamanian/American alternative rock band, formed in Panama City in 1993. The group was founded by Evan Rodaniche (guitar/vocals) and is currently based out of Los Angeles, California.
Cage9 has been direct openers for Ozzy Osbourne and Bad Religion, as well as shared the stage with notable acts like Queensrÿche, Candlebox, Seether, Sevendust, Hellyeah, Filter, In This Moment, Tesla, Karnivool, Buckcherry, MxPx, Powerman 5000, Dokken, Quiet Riot, Lynch Mob, Hinder, Boy Hits Car and Smile Empty Soul.
The band's song "My Doppelgänger (Doble Opuesto)," was released in English as well as Spanish and received full rotation on MTV Latino. The song "Hearts & Stars" is on the soundtrack to the video game MX vs. ATV: Untamed. Cage9 recorded a version of the theme song to The Dukes of Hazzard which was used in the trailer for the 2005 movie. The band also recorded music for a WWE promotion for Stone Cold Steve Austin and composed the Kamen Rider: Dragon Knight theme song, called "Let's Ride". On March 3, 2006, Cage9 made an appearance on G4's Attack of the Show!.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Cage9
309 Road
The 309 road is a 22-kilometre (14 mi) long gravel road between the towns of Coromandel and Whitianga in New Zealand.
The 309 winds its way from Coromandel, on the west side of the Coromandel Peninsula, over the ranges to Whitianga, on the eastern side.
The road is considered extremely dangerous and deaths among tourists unfamiliar with the road and in unfit vehicles are common.
Places of interest along the road include Waiau Falls and the Kauri Grove, a stand of mature kauri trees.
Location
References
External links
Coordinates: 36°50′48″S 175°33′15″E / 36.846767°S 175.554208°E / -36.846767; 175.554208 (309 Road - nominal location)
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/309_Road
List of highways numbered 44
The following highways are numbered 44.
Canada
Ontario Highway 44
India
Israel
Iran
Road 44
Japan
Route 44 (Japan)
New Zealand
New Zealand State Highway 44
Thailand
Thailand Route 44
United Arab Emirates
E 44
United Kingdom
British A44 (Oxford-Aberystwyth)
United States
Interstate 44
U.S. Route 44
Alabama State Route 44
California State Route 44
Colorado State Highway 44
Delaware Route 44
Florida State Road 44
Georgia State Route 44
Hawaii Route 44
Idaho State Highway 44
Illinois Route 44 (former)
Indiana State Road 44
Iowa Highway 44
K-44 (Kansas highway)
Kentucky Route 44
Louisiana Highway 44
Maryland Route 44 (former)
M-44 (Michigan highway)
Minnesota State Highway 44
Mississippi Highway 44
Montana Highway 44
Nebraska Highway 44
Nevada State Route 44 (former) New Jersey Route 44
New York State Route 44 (former)
-
New York State Route 44A (former)
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/List_of_highways_numbered_44
List of highways numbered 49
The following highways are numbered 49:
Canada
Highway 49 (Ontario)
India
Iran
Road 49
Japan
Route 49 (Japan)
New Zealand
New Zealand State Highway 49
United Kingdom
British A49 (Ross on Wye-Bamber Bridge)
British M49 (Severn Beach-Avonmouth)
United States
Interstate 49
U.S. Route 49
Alabama State Route 49
California State Route 49
Connecticut Route 49
Florida State Road 49
Georgia State Route 49
Illinois Route 49
Indiana State Road 49
K-49 (Kansas highway)
Kentucky Route 49
Louisiana Highway 49
Maryland Route 49
Massachusetts Route 49
M-49 (Michigan highway)
Minnesota State Highway 49 (former)
Missouri Route 49 (former)
Montana Highway 49
Nevada State Route 49 (former)
New Hampshire Route 49
New Jersey Route 49
New York State Route 49
North Carolina Highway 49
North Dakota Highway 49
Ohio State Route 49
Oklahoma State Highway 49
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/List_of_highways_numbered_49
Eminem Presents: The Re-Up
Eminem Presents: The Re-Up is a hip hop compilation album performed by various artists of American record label, Shady Records. The album features performances by Shady Records artists Eminem, D12, 50 Cent, Obie Trice, Stat Quo, Bobby Creekwater and Cashis, while affiliated artists such as Lloyd Banks, Akon and Nate Dogg, made guest appearances. The album debuted at number two on the US Billboard 200 chart and has since sold over one million copies in the US alone, being certified platinum by the RIAA.
Background
The album began as a street mixtape project; an underground, unofficial CD with raw production values. "But what happened is that the material was so good and the tracks were getting produced like a regular album", Eminem said: "Instead of putting it out there rough and unfinished, I thought we should add some other new tracks, make it a real album, and put it in the record stores to give these new artists a real boost".
Rampant misinformation about Eminem Presents: The Re-Up included many false internet track listings and the claim that the mixtape would be a tribute to the late Proof of D12. "The D12 album and those unreleased songs with Proof are coming", said Eminem, "but The Re-Up is about these new artists and these new songs. It isn't fair to them or to the memory of Proof to mix them up".
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Eminem_Presents:_The_Re-Up
List of The Honeymooners episodes
This article provides a list of all known sketches of The Honeymooners.
26 sketches were known to have aired in the 1951/52 season on DuMont's Cavalcade of Stars and two on The Ed Sullivan Show. The nine surviving episodes from Cavalcade have been released on DVD as of 2011. The two from The Ed Sullivan Show remain unreleased.
104 sketches were known to have aired between 1952-57 on CBS' The Jackie Gleason Show. Known as the "Lost Episodes", most of them have been released on DVD as of 2011. The remainder have not been released for various reasons, including: 1) Some are still lost or only in the hands of private collectors; 2) Some are incomplete or are in poor condition.
The "Classic 39" episodes are not included in this list as they constitute a sitcom version of The Honeymooners.
Cavalcade of Stars: 1951-52
The following is a listing of "Honeymooners" sketches that aired during the 1951-52 season of Cavalcade of Stars on the DuMont Television Network.
Additional lost DuMont episodes:
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/List_of_The_Honeymooners_episodes
Podcasts:
-
What are Moore Graphs and Cages? [Graph Theory]
This video introduces Moore graphs and explains their connection to cages. We will begin by looking at the degree-diameter problem, which allows us to derive the Moore bound and define Moore graphs. We then explore cages, regular graphs of minimum order with given girth and degree/valency, and show that all Moore graphs are cages. In future videos, we will explore cages further. If you would like to learn more on your own, here are some helpful resources: https://arxiv.org/abs/2010.13443 https://en.wikipedia.org/wiki/Moore_graph https://en.wikipedia.org/wiki/Cage_(graph_theory) https://mathworld.wolfram.com/CageGraph.html #graphtheory
published: 21 Mar 2022 -
Mind-Bending Animal Puzzle: Fit 12 Species into 6 Cages using Graph Theory!
Mind-Bending Animal Puzzle: Fit 12 Species into 6 Cages with Perfect Compatibility using Graph Theory! Join us for an exciting puzzle challenge as we explore Noah's Ark! In this brain-teasing scenario, Noah needs your help to assign 12 different species of animals to 6 cages while ensuring that each species only shares its space with compatible companions. Can we prove that there exists a solution where each species shares its cage with compatible companions? Join us on this journey of logical deduction and graph theory principles as we crack the code to this intriguing animal cage conundrum. Get ready to exercise your problem-solving skills and witness the power of graph theory in action! Let's dive in and unlock the secrets of this captivating puzzle together! In our previous video, we...
published: 12 Jun 2023 -
Construction of (r, g)-Graphs [Graph Theory]
This video examines a method of constructing regular graphs of any girth and degree. This method was originally used to prove that there exists an (r, g)-cage, or the smallest (r, g)-graph. For the source of the construction, check out this paper: https://www.semanticscholar.org/paper/Regular-Graphs-with-Given-Girth-and-Restricted-Sachs/35ed242db64dd50295b2df2061587c8be25e6642 00:00 Review 01:10 Base Cases 01:47 Proof setup 03:54 Proof Outline 04:05 Main Construction/Proof 12:04 Example 1 14:45 Example 2 15:24 Recursive Method 16:24 Recap Recommended Books: ******************************** Hypergraph Theory ******************************** "Hypergraph Theory: An Introduction": https://amzn.to/48WKqfy ******************************...
published: 25 Jun 2023 -
Modeling and Analysis of Small Cage Graphs: A New Algorithmic Approach
Modeling and Analysis of Small Cage Graphs: A New Algorithmic Approach View Book:- https://doi.org/10.9734/bpi/ratmcs/v4/6192B #Cage_graph #graph_theory #Heawood_graph #Petersen_graph #Robertson_graph
published: 02 Oct 2023 -
what is the meaning of cage
published: 10 Mar 2021 -
What is the multiway graph in Wolfram Physics?
In Episode 15: Where to apply Wolfram’s rules? https://www.youtube.com/watch?v=kW-nr7ehVlM I introduced a radical idea. When we’re applying a rule to a graph in Wolfram Physics, there are generally many possible places in the graph we could apply the rule, giving us many possible next states of the universe. Here’s the radical idea: rather than choose one of these possible universes, we choose not to choose. Instead, we keep each of them in mind. The trouble is, if we choose not to choose, the number of possible universes we have to keep in mind gets extremely large extremely quickly. To help us visualize all these possible universes, we’re going to need the multiway graph. It’s a crucial idea in Wolfram Physics. The multiway graph will allow us to derive aspects of quantum mechanics...
published: 01 Dec 2022 -
Diego González Moreno - On cages and its generalizations
published: 10 Nov 2022 -
𝐂𝐇𝐀𝐏𝐓𝐄𝐑 6 : 𝐓𝐇𝐄 𝐌𝐀𝐓𝐇𝐄𝐌𝐀𝐓𝐈𝐂𝐒 𝐎𝐅 𝐆𝐑𝐀𝐏𝐇𝐒 | 𝐏𝐄𝐍 𝐓𝐑𝐀𝐂𝐈𝐍𝐆 𝐏𝐔𝐙𝐙𝐋𝐄 𝐀𝐍𝐃 𝐆𝐑𝐀𝐏𝐇 𝐂𝐎𝐋𝐎𝐑𝐈𝐍𝐆
Good day everyone, Welcome to our Channel ! The Tribe 5 Interval proudly presents to you our video discussion about Chapter 6: The Mathemaritcs of Graphs | Pen Tracing Puzzle and Graph Coloring. In this video lesson, we will learn about how to trace a given shape, Each vertex need be colored and cannot be given the same color. Please don't forget to like, share, subscribe and click the notification bell for more updates and for more upcoming videos. Thank you !!! Tribe 5 Interval Tribe Leader: Arillas, Kristine F. Tribe Secretary: Sernal, Angel Aubrey S. Editor: Bermundo, Janine T. Instructor: Mary Boths Bonador Reporters: 1. Servillon, Bea Bernice Victoria •Pen-Tracing Puzzles 2. Albao, Francia Joy O. •Transportation 3. Bermundo, Janine T. •Finding the graphs 4. Guerre...
published: 05 Oct 2021 -
Structural Graph Theory 2021 Lecture-23
In today's lecture (11/03/2021): 1. We proved Euler's Formula and discussed a few of its consequences. In particular, we observed that, for a planar graph G, (i) the number of faces (in any planar embedding of G) is an invariant (i.e., it does not depend on the embedding) and (ii) if G is simple then e(G) is upper bounded by 3 v(G) - 6. 2. We saw an intuitive way of thinking about the 'bridges of a cycle', and described them formally, and discussed some terminology pertaining to bridges. We shall find these concepts useful in proving (i) that every simple 3-connected planar graph has a unique planar embedding and (ii) Kuratowski's Theorem.
published: 11 Mar 2021 -
Štefan Gyürki, Extremal bipartite biregular bi coset graphs
The main goal of the Workshop is to embrace recent results in developing Algebraic Graph Theory and its Applications. We are interested in algebraic, spectral and structural characterisation of highly regular graphs, investigating graphs defined on groups, constructing new graphs, codes and designs. The workshop is organized by Mathematical Center in Akademgorodok in cooperation with the Sino-Russian Mathematics Center at Peking University in Beijing and the Three Gorges Mathematical Research Center at China Three Gorges University in Yichang. http://mca.nsu.ru/agt7/
published: 30 Nov 2022
developed with YouTube
14:40
What are Moore Graphs and Cages? [Graph Theory]
- Order: Reorder
- Duration: 14:40
- Uploaded Date: 21 Mar 2022
- views: 1074
This video introduces Moore graphs and explains their connection to cages. We will begin by looking at the degree-diameter problem, which allows us to derive th...
This video introduces Moore graphs and explains their connection to cages. We will begin by looking at the degree-diameter problem, which allows us to derive the Moore bound and define Moore graphs. We then explore cages, regular graphs of minimum order with given girth and degree/valency, and show that all Moore graphs are cages. In future videos, we will explore cages further. If you would like to learn more on your own, here are some helpful resources:
https://arxiv.org/abs/2010.13443
https://en.wikipedia.org/wiki/Moore_graph
https://en.wikipedia.org/wiki/Cage_(graph_theory)
https://mathworld.wolfram.com/CageGraph.html
#graphtheory
https://wn.com/What_Are_Moore_Graphs_And_Cages_Graph_Theory
This video introduces Moore graphs and explains their connection to cages. We will begin by looking at the degree-diameter problem, which allows us to derive the Moore bound and define Moore graphs. We then explore cages, regular graphs of minimum order with given girth and degree/valency, and show that all Moore graphs are cages. In future videos, we will explore cages further. If you would like to learn more on your own, here are some helpful resources:
https://arxiv.org/abs/2010.13443
https://en.wikipedia.org/wiki/Moore_graph
https://en.wikipedia.org/wiki/Cage_(graph_theory)
https://mathworld.wolfram.com/CageGraph.html
#graphtheory
7:42
Mind-Bending Animal Puzzle: Fit 12 Species into 6 Cages using Graph Theory!
- Order: Reorder
- Duration: 7:42
- Uploaded Date: 12 Jun 2023
- views: 53
Mind-Bending Animal Puzzle: Fit 12 Species into 6 Cages with Perfect Compatibility using Graph Theory!
Join us for an exciting puzzle challenge as we explore N...
Mind-Bending Animal Puzzle: Fit 12 Species into 6 Cages with Perfect Compatibility using Graph Theory!
Join us for an exciting puzzle challenge as we explore Noah's Ark! In this brain-teasing scenario, Noah needs your help to assign 12 different species of animals to 6 cages while ensuring that each species only shares its space with compatible companions. Can we prove that there exists a solution where each species shares its cage with compatible companions? Join us on this journey of logical deduction and graph theory principles as we crack the code to this intriguing animal cage conundrum. Get ready to exercise your problem-solving skills and witness the power of graph theory in action! Let's dive in and unlock the secrets of this captivating puzzle together!
In our previous video, we explored how graph theory can be applied to solve complex problems, leaving you with an intriguing puzzle to ponder.
In this highly anticipated follow-up, we're back to conquer yet another challenging puzzle using the elegant principles of graph theory. Watch as we unravel the secrets hidden within the graph, employing strategic thinking and problem-solving skills to crack the code.
But that's not all! If you missed our previous video, fret not! The link to the video is provided below, allowing you to catch up on the fascinating journey of applying graph theory to solve a mind-bending puzzle.
https://youtu.be/86LW5-zEFKc
Prepare to be captivated, inspired, and challenged as we showcase the incredible power of graph theory in unraveling complex puzzles. Don't forget to bring your enthusiasm and join us on this intellectual adventure!
VIDEO credits:
href="https://www.freepik.com/free-video/cgi-animation-of-pulsating-dots-and-messaging-icons-connected-by-strings-floating-in-dark-digital-space-with-plexus-effect_171057#position=8&term;=network%20graph%20cycles&from;_view=search" Video by Freepik
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Video by Freepik
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IMAGE credits:
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MUSIC credits:
Music by href="https://pixabay.com/users/the_mountain-3616498/?utm_source=link-attribution&utm;_medium=referral&utm;_campaign=music&utm;_content=136110" The_Mountain
from href="https://pixabay.com/music//?utm_source=link-attribution&utm;_medium=referral&utm;_campaign=music&utm;_content=136110" Pixabay
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https://wn.com/Mind_Bending_Animal_Puzzle_Fit_12_Species_Into_6_Cages_Using_Graph_Theory
Mind-Bending Animal Puzzle: Fit 12 Species into 6 Cages with Perfect Compatibility using Graph Theory!
Join us for an exciting puzzle challenge as we explore Noah's Ark! In this brain-teasing scenario, Noah needs your help to assign 12 different species of animals to 6 cages while ensuring that each species only shares its space with compatible companions. Can we prove that there exists a solution where each species shares its cage with compatible companions? Join us on this journey of logical deduction and graph theory principles as we crack the code to this intriguing animal cage conundrum. Get ready to exercise your problem-solving skills and witness the power of graph theory in action! Let's dive in and unlock the secrets of this captivating puzzle together!
In our previous video, we explored how graph theory can be applied to solve complex problems, leaving you with an intriguing puzzle to ponder.
In this highly anticipated follow-up, we're back to conquer yet another challenging puzzle using the elegant principles of graph theory. Watch as we unravel the secrets hidden within the graph, employing strategic thinking and problem-solving skills to crack the code.
But that's not all! If you missed our previous video, fret not! The link to the video is provided below, allowing you to catch up on the fascinating journey of applying graph theory to solve a mind-bending puzzle.
https://youtu.be/86LW5-zEFKc
Prepare to be captivated, inspired, and challenged as we showcase the incredible power of graph theory in unraveling complex puzzles. Don't forget to bring your enthusiasm and join us on this intellectual adventure!
VIDEO credits:
href="https://www.freepik.com/free-video/cgi-animation-of-pulsating-dots-and-messaging-icons-connected-by-strings-floating-in-dark-digital-space-with-plexus-effect_171057#position=8&term;=network%20graph%20cycles&from;_view=search" Video by Freepik
href="https://www.freepik.com/free-video/connections-futuristic-3d-geometry-structure-loop_179359#position=9&term;=geometric%20graph&from;_view=search"
Video by Freepik
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IMAGE credits:
href="https://www.freepik.com/free-photo/3d-colourful-low-poly-plexus-design-with-shallow-depth-field_9760725.htm#page=15&query;=network%20graph&position;=45&from;_view=search&track;=ais" Image by kjpargeter on Freepik
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- published: 12 Jun 2023
- views: 53
17:09
Construction of (r, g)-Graphs [Graph Theory]
- Order: Reorder
- Duration: 17:09
- Uploaded Date: 25 Jun 2023
- views: 149
This video examines a method of constructing regular graphs of any girth and degree. This method was originally used to prove that there exists an (r, g)-cage, ...
This video examines a method of constructing regular graphs of any girth and degree. This method was originally used to prove that there exists an (r, g)-cage, or the smallest (r, g)-graph.
For the source of the construction, check out this paper:
https://www.semanticscholar.org/paper/Regular-Graphs-with-Given-Girth-and-Restricted-Sachs/35ed242db64dd50295b2df2061587c8be25e6642
00:00 Review
01:10 Base Cases
01:47 Proof setup
03:54 Proof Outline
04:05 Main Construction/Proof
12:04 Example 1
14:45 Example 2
15:24 Recursive Method
16:24 Recap
Recommended Books:
******************************** Hypergraph Theory ********************************
"Hypergraph Theory: An Introduction": https://amzn.to/48WKqfy
******************************** Graph Theory ********************************
"Introduction to Graph Theory (Trudeau)": https://amzn.to/48ZWhtj
"Graph Theory (Diestel)": https://amzn.to/4aYCSdW
******************************** Misc. Undergraduate Mathematics ********************************
Discrete Mathematics with Applications (Epp): https://amzn.to/4aWC1dM
A Book of Abstract Algebra (Pinter): https://amzn.to/3S2QmfV
Language, Proof and Logic: https://amzn.to/47EIZkE
Linear Algebra and Its Applications: https://amzn.to/48QsoMt
All the Math You Missed: https://amzn.to/3u5dORP
These are my Amazon Affiliate links. As an Amazon Associate I may earn commissions for purchases made through the links above.
#graphtheory
#mathematics
#vitalsine
https://wn.com/Construction_Of_(R,_G)_Graphs_Graph_Theory
This video examines a method of constructing regular graphs of any girth and degree. This method was originally used to prove that there exists an (r, g)-cage, or the smallest (r, g)-graph.
For the source of the construction, check out this paper:
https://www.semanticscholar.org/paper/Regular-Graphs-with-Given-Girth-and-Restricted-Sachs/35ed242db64dd50295b2df2061587c8be25e6642
00:00 Review
01:10 Base Cases
01:47 Proof setup
03:54 Proof Outline
04:05 Main Construction/Proof
12:04 Example 1
14:45 Example 2
15:24 Recursive Method
16:24 Recap
Recommended Books:
******************************** Hypergraph Theory ********************************
"Hypergraph Theory: An Introduction": https://amzn.to/48WKqfy
******************************** Graph Theory ********************************
"Introduction to Graph Theory (Trudeau)": https://amzn.to/48ZWhtj
"Graph Theory (Diestel)": https://amzn.to/4aYCSdW
******************************** Misc. Undergraduate Mathematics ********************************
Discrete Mathematics with Applications (Epp): https://amzn.to/4aWC1dM
A Book of Abstract Algebra (Pinter): https://amzn.to/3S2QmfV
Language, Proof and Logic: https://amzn.to/47EIZkE
Linear Algebra and Its Applications: https://amzn.to/48QsoMt
All the Math You Missed: https://amzn.to/3u5dORP
These are my Amazon Affiliate links. As an Amazon Associate I may earn commissions for purchases made through the links above.
#graphtheory
#mathematics
#vitalsine
- published: 25 Jun 2023
- views: 149
5:28
Modeling and Analysis of Small Cage Graphs: A New Algorithmic Approach
- Order: Reorder
- Duration: 5:28
- Uploaded Date: 02 Oct 2023
- views: 6
Modeling and Analysis of Small Cage Graphs: A New Algorithmic Approach
View Book:- https://doi.org/10.9734/bpi/ratmcs/v4/6192B
#Cage_graph #graph_theory #Heawo...
Modeling and Analysis of Small Cage Graphs: A New Algorithmic Approach
View Book:- https://doi.org/10.9734/bpi/ratmcs/v4/6192B
#Cage_graph #graph_theory #Heawood_graph #Petersen_graph #Robertson_graph
https://wn.com/Modeling_And_Analysis_Of_Small_Cage_Graphs_A_New_Algorithmic_Approach
Modeling and Analysis of Small Cage Graphs: A New Algorithmic Approach
View Book:- https://doi.org/10.9734/bpi/ratmcs/v4/6192B
#Cage_graph #graph_theory #Heawood_graph #Petersen_graph #Robertson_graph
- published: 02 Oct 2023
- views: 6
1:50
what is the meaning of cage
- Order: Reorder
- Duration: 1:50
- Uploaded Date: 10 Mar 2021
- views: 3
- published: 10 Mar 2021
- views: 3
12:13
What is the multiway graph in Wolfram Physics?
- Order: Reorder
- Duration: 12:13
- Uploaded Date: 01 Dec 2022
- views: 2621
In Episode 15: Where to apply Wolfram’s rules? https://www.youtube.com/watch?v=kW-nr7ehVlM I introduced a radical idea.
When we’re applying a rule to a graph i...
In Episode 15: Where to apply Wolfram’s rules? https://www.youtube.com/watch?v=kW-nr7ehVlM I introduced a radical idea.
When we’re applying a rule to a graph in Wolfram Physics, there are generally many possible places in the graph we could apply the rule, giving us many possible next states of the universe.
Here’s the radical idea: rather than choose one of these possible universes, we choose not to choose. Instead, we keep each of them in mind.
The trouble is, if we choose not to choose, the number of possible universes we have to keep in mind gets extremely large extremely quickly.
To help us visualize all these possible universes, we’re going to need the multiway graph.
It’s a crucial idea in Wolfram Physics.
The multiway graph will allow us to derive aspects of quantum mechanics from Wolfram Physics.
It’ll lead us to a concept of the observer that promises to resolve issues related to the collapse of the wavefunction that have plagued quantum mechanics ever since Schrödinger put his metaphorical cat into a metaphorical cage.
And maybe, just maybe, it’ll lead us to a model of consciousness itself.
–
Prefer to listen to the audio? Search for The Last Theory in your podcast player, or listen at https://lasttheory.com/podcast/023-what-is-the-multiway-graph-in-wolfram-physics
The full article is at https://lasttheory.com/article/what-is-the-multiway-graph-in-wolfram-physics
Kootenay Village Ventures Inc.
https://wn.com/What_Is_The_Multiway_Graph_In_Wolfram_Physics
In Episode 15: Where to apply Wolfram’s rules? https://www.youtube.com/watch?v=kW-nr7ehVlM I introduced a radical idea.
When we’re applying a rule to a graph in Wolfram Physics, there are generally many possible places in the graph we could apply the rule, giving us many possible next states of the universe.
Here’s the radical idea: rather than choose one of these possible universes, we choose not to choose. Instead, we keep each of them in mind.
The trouble is, if we choose not to choose, the number of possible universes we have to keep in mind gets extremely large extremely quickly.
To help us visualize all these possible universes, we’re going to need the multiway graph.
It’s a crucial idea in Wolfram Physics.
The multiway graph will allow us to derive aspects of quantum mechanics from Wolfram Physics.
It’ll lead us to a concept of the observer that promises to resolve issues related to the collapse of the wavefunction that have plagued quantum mechanics ever since Schrödinger put his metaphorical cat into a metaphorical cage.
And maybe, just maybe, it’ll lead us to a model of consciousness itself.
–
Prefer to listen to the audio? Search for The Last Theory in your podcast player, or listen at https://lasttheory.com/podcast/023-what-is-the-multiway-graph-in-wolfram-physics
The full article is at https://lasttheory.com/article/what-is-the-multiway-graph-in-wolfram-physics
Kootenay Village Ventures Inc.
- published: 01 Dec 2022
- views: 2621
44:24
Diego González Moreno - On cages and its generalizations
- Order: Reorder
- Duration: 44:24
- Uploaded Date: 10 Nov 2022
- views: 37
- published: 10 Nov 2022
- views: 37
20:29
𝐂𝐇𝐀𝐏𝐓𝐄𝐑 6 : 𝐓𝐇𝐄 𝐌𝐀𝐓𝐇𝐄𝐌𝐀𝐓𝐈𝐂𝐒 𝐎𝐅 𝐆𝐑𝐀𝐏𝐇𝐒 | 𝐏𝐄𝐍 𝐓𝐑𝐀𝐂𝐈𝐍𝐆 𝐏𝐔𝐙𝐙𝐋𝐄 𝐀𝐍𝐃 𝐆𝐑𝐀𝐏𝐇 𝐂𝐎𝐋𝐎𝐑𝐈𝐍𝐆
- Order: Reorder
- Duration: 20:29
- Uploaded Date: 05 Oct 2021
- views: 299
Good day everyone, Welcome to our Channel !
The Tribe 5 Interval proudly presents to you our video discussion about Chapter 6: The Mathemaritcs of Graphs | Pen...
Good day everyone, Welcome to our Channel !
The Tribe 5 Interval proudly presents to you our video discussion about Chapter 6: The Mathemaritcs of Graphs | Pen Tracing Puzzle and Graph Coloring.
In this video lesson, we will learn about how to trace a given shape, Each vertex need be colored and cannot be given the same color.
Please don't forget to like, share, subscribe and click the notification bell for more updates and for more upcoming videos. Thank you !!!
Tribe 5 Interval
Tribe Leader: Arillas, Kristine F.
Tribe Secretary: Sernal, Angel Aubrey S.
Editor: Bermundo, Janine T.
Instructor: Mary Boths Bonador
Reporters:
1. Servillon, Bea Bernice Victoria
•Pen-Tracing Puzzles
2. Albao, Francia Joy O.
•Transportation
3. Bermundo, Janine T.
•Finding the graphs
4. Guerrero, Tei S.
•Social Networks
5. Lauderez, Ladymer S.
•Graph Coloring and Vertex
Coloring
6. Periabras, Andrea B.
•Chromatic Number
7. Manangat, Maria Josefa R.
•Region Coloring
https://wn.com/𝐂𝐇𝐀𝐏𝐓𝐄𝐑_6_𝐓𝐇𝐄_𝐌𝐀𝐓𝐇𝐄𝐌𝐀𝐓𝐈𝐂𝐒_𝐎𝐅_𝐆𝐑𝐀𝐏𝐇𝐒_|_𝐏𝐄𝐍_𝐓𝐑𝐀𝐂𝐈𝐍𝐆_𝐏𝐔𝐙𝐙𝐋𝐄_𝐀𝐍𝐃_𝐆𝐑𝐀𝐏𝐇_𝐂𝐎𝐋𝐎𝐑𝐈𝐍𝐆
Good day everyone, Welcome to our Channel !
The Tribe 5 Interval proudly presents to you our video discussion about Chapter 6: The Mathemaritcs of Graphs | Pen Tracing Puzzle and Graph Coloring.
In this video lesson, we will learn about how to trace a given shape, Each vertex need be colored and cannot be given the same color.
Please don't forget to like, share, subscribe and click the notification bell for more updates and for more upcoming videos. Thank you !!!
Tribe 5 Interval
Tribe Leader: Arillas, Kristine F.
Tribe Secretary: Sernal, Angel Aubrey S.
Editor: Bermundo, Janine T.
Instructor: Mary Boths Bonador
Reporters:
1. Servillon, Bea Bernice Victoria
•Pen-Tracing Puzzles
2. Albao, Francia Joy O.
•Transportation
3. Bermundo, Janine T.
•Finding the graphs
4. Guerrero, Tei S.
•Social Networks
5. Lauderez, Ladymer S.
•Graph Coloring and Vertex
Coloring
6. Periabras, Andrea B.
•Chromatic Number
7. Manangat, Maria Josefa R.
•Region Coloring
- published: 05 Oct 2021
- views: 299
57:01
Structural Graph Theory 2021 Lecture-23
- Order: Reorder
- Duration: 57:01
- Uploaded Date: 11 Mar 2021
- views: 66
In today's lecture (11/03/2021):
1. We proved Euler's Formula and discussed a few of its consequences. In particular, we observed that, for a planar graph G, (...
In today's lecture (11/03/2021):
1. We proved Euler's Formula and discussed a few of its consequences. In particular, we observed that, for a planar graph G, (i) the number of faces (in any planar embedding of G) is an invariant (i.e., it does not depend on the embedding) and (ii) if G is simple then e(G) is upper bounded by 3 v(G) - 6.
2. We saw an intuitive way of thinking about the 'bridges of a cycle', and described them formally, and discussed some terminology pertaining to bridges. We shall find these concepts useful in proving (i) that every simple 3-connected planar graph has a unique planar embedding and (ii) Kuratowski's Theorem.
https://wn.com/Structural_Graph_Theory_2021_Lecture_23
In today's lecture (11/03/2021):
1. We proved Euler's Formula and discussed a few of its consequences. In particular, we observed that, for a planar graph G, (i) the number of faces (in any planar embedding of G) is an invariant (i.e., it does not depend on the embedding) and (ii) if G is simple then e(G) is upper bounded by 3 v(G) - 6.
2. We saw an intuitive way of thinking about the 'bridges of a cycle', and described them formally, and discussed some terminology pertaining to bridges. We shall find these concepts useful in proving (i) that every simple 3-connected planar graph has a unique planar embedding and (ii) Kuratowski's Theorem.
- published: 11 Mar 2021
- views: 66
53:23
Štefan Gyürki, Extremal bipartite biregular bi coset graphs
- Order: Reorder
- Duration: 53:23
- Uploaded Date: 30 Nov 2022
- views: 153
The main goal of the Workshop is to embrace recent results in developing Algebraic Graph Theory and its Applications. We are interested in algebraic, spectral a...
The main goal of the Workshop is to embrace recent results in developing Algebraic Graph Theory and its Applications. We are interested in algebraic, spectral and structural characterisation of highly regular graphs, investigating graphs defined on groups, constructing new graphs, codes and designs.
The workshop is organized by Mathematical Center in Akademgorodok in cooperation with the Sino-Russian Mathematics Center at Peking University in Beijing and the Three Gorges Mathematical Research Center at China Three Gorges University in Yichang.
http://mca.nsu.ru/agt7/
https://wn.com/ŠTefan_GyüRki,_Extremal_Bipartite_Biregular_Bi_Coset_Graphs
The main goal of the Workshop is to embrace recent results in developing Algebraic Graph Theory and its Applications. We are interested in algebraic, spectral and structural characterisation of highly regular graphs, investigating graphs defined on groups, constructing new graphs, codes and designs.
The workshop is organized by Mathematical Center in Akademgorodok in cooperation with the Sino-Russian Mathematics Center at Peking University in Beijing and the Three Gorges Mathematical Research Center at China Three Gorges University in Yichang.
http://mca.nsu.ru/agt7/
- published: 30 Nov 2022
- views: 153
14:40
What are Moore Graphs and Cages? [Graph Theory]
This video introduces Moore graphs and explains their connection to cages. We will begin b...
published: 21 Mar 2022
What are Moore Graphs and Cages? [Graph Theory]
What are Moore Graphs and Cages? [Graph Theory]
- Report rights infringement
- published: 21 Mar 2022
- views: 1074
This video introduces Moore graphs and explains their connection to cages. We will begin by looking at the degree-diameter problem, which allows us to derive the Moore bound and define Moore graphs. We then explore cages, regular graphs of minimum order with given girth and degree/valency, and show that all Moore graphs are cages. In future videos, we will explore cages further. If you would like to learn more on your own, here are some helpful resources:
https://arxiv.org/abs/2010.13443
https://en.wikipedia.org/wiki/Moore_graph
https://en.wikipedia.org/wiki/Cage_(graph_theory)
https://mathworld.wolfram.com/CageGraph.html
#graphtheory
7:42
Mind-Bending Animal Puzzle: Fit 12 Species into 6 Cages using Graph Theory!
Mind-Bending Animal Puzzle: Fit 12 Species into 6 Cages with Perfect Compatibility using G...
published: 12 Jun 2023
Mind-Bending Animal Puzzle: Fit 12 Species into 6 Cages using Graph Theory!
Mind-Bending Animal Puzzle: Fit 12 Species into 6 Cages using Graph Theory!
- Report rights infringement
- published: 12 Jun 2023
- views: 53
Mind-Bending Animal Puzzle: Fit 12 Species into 6 Cages with Perfect Compatibility using Graph Theory!
Join us for an exciting puzzle challenge as we explore Noah's Ark! In this brain-teasing scenario, Noah needs your help to assign 12 different species of animals to 6 cages while ensuring that each species only shares its space with compatible companions. Can we prove that there exists a solution where each species shares its cage with compatible companions? Join us on this journey of logical deduction and graph theory principles as we crack the code to this intriguing animal cage conundrum. Get ready to exercise your problem-solving skills and witness the power of graph theory in action! Let's dive in and unlock the secrets of this captivating puzzle together!
In our previous video, we explored how graph theory can be applied to solve complex problems, leaving you with an intriguing puzzle to ponder.
In this highly anticipated follow-up, we're back to conquer yet another challenging puzzle using the elegant principles of graph theory. Watch as we unravel the secrets hidden within the graph, employing strategic thinking and problem-solving skills to crack the code.
But that's not all! If you missed our previous video, fret not! The link to the video is provided below, allowing you to catch up on the fascinating journey of applying graph theory to solve a mind-bending puzzle.
https://youtu.be/86LW5-zEFKc
Prepare to be captivated, inspired, and challenged as we showcase the incredible power of graph theory in unraveling complex puzzles. Don't forget to bring your enthusiasm and join us on this intellectual adventure!
VIDEO credits:
href="https://www.freepik.com/free-video/cgi-animation-of-pulsating-dots-and-messaging-icons-connected-by-strings-floating-in-dark-digital-space-with-plexus-effect_171057#position=8&term;=network%20graph%20cycles&from;_view=search" Video by Freepik
href="https://www.freepik.com/free-video/connections-futuristic-3d-geometry-structure-loop_179359#position=9&term;=geometric%20graph&from;_view=search"
Video by Freepik
Video by href="https://pixabay.com/users/md579-22245022/?utm_source=link-attribution&utm;_medium=referral&utm;_campaign=video&utm;_content=79087" md579 from
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from
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Hai Diep
from href="https://pixabay.com//?utm_source=link-attribution&utm;_medium=referral&utm;_campaign=video&utm;_content=158980" Pixabay
IMAGE credits:
href="https://www.freepik.com/free-photo/3d-colourful-low-poly-plexus-design-with-shallow-depth-field_9760725.htm#page=15&query;=network%20graph&position;=45&from;_view=search&track;=ais" Image by kjpargeter on Freepik
Image by href="https://www.freepik.com/free-vector/gradient-network-connection-background_12704437.htm#page=14&query;=network%20graph&position;=23&from;_view=search&track;=ais" Freepik
href="https://www.freepik.com/free-photo/abstract-background-with-low-poly-design_2795509.htm#page=12&query;=network%20graph&position;=35&from;_view=search&track;=ais" Image by kjpargeter on Freepik
href="https://www.freepik.com/free-photo/abstract-plexus-blue-geometrical-shapes-connection-ai-generated-image_41111846.htm#page=9&query;=network%20graph&position;=5&from;_view=search&track;=ais" Image by ojosujono96 on Freepik
MUSIC credits:
Music by href="https://pixabay.com/users/the_mountain-3616498/?utm_source=link-attribution&utm;_medium=referral&utm;_campaign=music&utm;_content=136110" The_Mountain
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from href="https://pixabay.com/music//?utm_source=link-attribution&utm;_medium=referral&utm;_campaign=music&utm;_content=93793" Pixabay
17:09
Construction of (r, g)-Graphs [Graph Theory]
This video examines a method of constructing regular graphs of any girth and degree. This ...
published: 25 Jun 2023
Construction of (r, g)-Graphs [Graph Theory]
Construction of (r, g)-Graphs [Graph Theory]
- Report rights infringement
- published: 25 Jun 2023
- views: 149
This video examines a method of constructing regular graphs of any girth and degree. This method was originally used to prove that there exists an (r, g)-cage, or the smallest (r, g)-graph.
For the source of the construction, check out this paper:
https://www.semanticscholar.org/paper/Regular-Graphs-with-Given-Girth-and-Restricted-Sachs/35ed242db64dd50295b2df2061587c8be25e6642
00:00 Review
01:10 Base Cases
01:47 Proof setup
03:54 Proof Outline
04:05 Main Construction/Proof
12:04 Example 1
14:45 Example 2
15:24 Recursive Method
16:24 Recap
Recommended Books:
******************************** Hypergraph Theory ********************************
"Hypergraph Theory: An Introduction": https://amzn.to/48WKqfy
******************************** Graph Theory ********************************
"Introduction to Graph Theory (Trudeau)": https://amzn.to/48ZWhtj
"Graph Theory (Diestel)": https://amzn.to/4aYCSdW
******************************** Misc. Undergraduate Mathematics ********************************
Discrete Mathematics with Applications (Epp): https://amzn.to/4aWC1dM
A Book of Abstract Algebra (Pinter): https://amzn.to/3S2QmfV
Language, Proof and Logic: https://amzn.to/47EIZkE
Linear Algebra and Its Applications: https://amzn.to/48QsoMt
All the Math You Missed: https://amzn.to/3u5dORP
These are my Amazon Affiliate links. As an Amazon Associate I may earn commissions for purchases made through the links above.
#graphtheory
#mathematics
#vitalsine
5:28
Modeling and Analysis of Small Cage Graphs: A New Algorithmic Approach
Modeling and Analysis of Small Cage Graphs: A New Algorithmic Approach
View Book:- https:...
published: 02 Oct 2023
Modeling and Analysis of Small Cage Graphs: A New Algorithmic Approach
Modeling and Analysis of Small Cage Graphs: A New Algorithmic Approach
- Report rights infringement
- published: 02 Oct 2023
- views: 6
Modeling and Analysis of Small Cage Graphs: A New Algorithmic Approach
View Book:- https://doi.org/10.9734/bpi/ratmcs/v4/6192B
#Cage_graph #graph_theory #Heawood_graph #Petersen_graph #Robertson_graph
1:50
what is the meaning of cage
published: 10 Mar 2021
what is the meaning of cage
12:13
What is the multiway graph in Wolfram Physics?
In Episode 15: Where to apply Wolfram’s rules? https://www.youtube.com/watch?v=kW-nr7ehVlM...
published: 01 Dec 2022
What is the multiway graph in Wolfram Physics?
What is the multiway graph in Wolfram Physics?
- Report rights infringement
- published: 01 Dec 2022
- views: 2621
In Episode 15: Where to apply Wolfram’s rules? https://www.youtube.com/watch?v=kW-nr7ehVlM I introduced a radical idea.
When we’re applying a rule to a graph in Wolfram Physics, there are generally many possible places in the graph we could apply the rule, giving us many possible next states of the universe.
Here’s the radical idea: rather than choose one of these possible universes, we choose not to choose. Instead, we keep each of them in mind.
The trouble is, if we choose not to choose, the number of possible universes we have to keep in mind gets extremely large extremely quickly.
To help us visualize all these possible universes, we’re going to need the multiway graph.
It’s a crucial idea in Wolfram Physics.
The multiway graph will allow us to derive aspects of quantum mechanics from Wolfram Physics.
It’ll lead us to a concept of the observer that promises to resolve issues related to the collapse of the wavefunction that have plagued quantum mechanics ever since Schrödinger put his metaphorical cat into a metaphorical cage.
And maybe, just maybe, it’ll lead us to a model of consciousness itself.
–
Prefer to listen to the audio? Search for The Last Theory in your podcast player, or listen at https://lasttheory.com/podcast/023-what-is-the-multiway-graph-in-wolfram-physics
The full article is at https://lasttheory.com/article/what-is-the-multiway-graph-in-wolfram-physics
Kootenay Village Ventures Inc.
44:24
Diego González Moreno - On cages and its generalizations
published: 10 Nov 2022
Diego González Moreno - On cages and its generalizations
Diego González Moreno - On cages and its generalizations
- Report rights infringement
- published: 10 Nov 2022
- views: 37
20:29
𝐂𝐇𝐀𝐏𝐓𝐄𝐑 6 : 𝐓𝐇𝐄 𝐌𝐀𝐓𝐇𝐄𝐌𝐀𝐓𝐈𝐂𝐒 𝐎𝐅 𝐆𝐑𝐀𝐏𝐇𝐒 | 𝐏𝐄𝐍 𝐓𝐑𝐀𝐂𝐈𝐍𝐆 𝐏𝐔𝐙𝐙𝐋𝐄 𝐀𝐍𝐃 𝐆𝐑𝐀𝐏𝐇 𝐂𝐎𝐋𝐎𝐑𝐈𝐍𝐆
Good day everyone, Welcome to our Channel !
The Tribe 5 Interval proudly presents to you ...
published: 05 Oct 2021
𝐂𝐇𝐀𝐏𝐓𝐄𝐑 6 : 𝐓𝐇𝐄 𝐌𝐀𝐓𝐇𝐄𝐌𝐀𝐓𝐈𝐂𝐒 𝐎𝐅 𝐆𝐑𝐀𝐏𝐇𝐒 | 𝐏𝐄𝐍 𝐓𝐑𝐀𝐂𝐈𝐍𝐆 𝐏𝐔𝐙𝐙𝐋𝐄 𝐀𝐍𝐃 𝐆𝐑𝐀𝐏𝐇 𝐂𝐎𝐋𝐎𝐑𝐈𝐍𝐆
𝐂𝐇𝐀𝐏𝐓𝐄𝐑 6 : 𝐓𝐇𝐄 𝐌𝐀𝐓𝐇𝐄𝐌𝐀𝐓𝐈𝐂𝐒 𝐎𝐅 𝐆𝐑𝐀𝐏𝐇𝐒 | 𝐏𝐄𝐍 𝐓𝐑𝐀𝐂𝐈𝐍𝐆 𝐏𝐔𝐙𝐙𝐋𝐄 𝐀𝐍𝐃 𝐆𝐑𝐀𝐏𝐇 𝐂𝐎𝐋𝐎𝐑𝐈𝐍𝐆
- Report rights infringement
- published: 05 Oct 2021
- views: 299
Good day everyone, Welcome to our Channel !
The Tribe 5 Interval proudly presents to you our video discussion about Chapter 6: The Mathemaritcs of Graphs | Pen Tracing Puzzle and Graph Coloring.
In this video lesson, we will learn about how to trace a given shape, Each vertex need be colored and cannot be given the same color.
Please don't forget to like, share, subscribe and click the notification bell for more updates and for more upcoming videos. Thank you !!!
Tribe 5 Interval
Tribe Leader: Arillas, Kristine F.
Tribe Secretary: Sernal, Angel Aubrey S.
Editor: Bermundo, Janine T.
Instructor: Mary Boths Bonador
Reporters:
1. Servillon, Bea Bernice Victoria
•Pen-Tracing Puzzles
2. Albao, Francia Joy O.
•Transportation
3. Bermundo, Janine T.
•Finding the graphs
4. Guerrero, Tei S.
•Social Networks
5. Lauderez, Ladymer S.
•Graph Coloring and Vertex
Coloring
6. Periabras, Andrea B.
•Chromatic Number
7. Manangat, Maria Josefa R.
•Region Coloring
57:01
Structural Graph Theory 2021 Lecture-23
In today's lecture (11/03/2021):
1. We proved Euler's Formula and discussed a few of its ...
published: 11 Mar 2021
Structural Graph Theory 2021 Lecture-23
Structural Graph Theory 2021 Lecture-23
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- published: 11 Mar 2021
- views: 66
In today's lecture (11/03/2021):
1. We proved Euler's Formula and discussed a few of its consequences. In particular, we observed that, for a planar graph G, (i) the number of faces (in any planar embedding of G) is an invariant (i.e., it does not depend on the embedding) and (ii) if G is simple then e(G) is upper bounded by 3 v(G) - 6.
2. We saw an intuitive way of thinking about the 'bridges of a cycle', and described them formally, and discussed some terminology pertaining to bridges. We shall find these concepts useful in proving (i) that every simple 3-connected planar graph has a unique planar embedding and (ii) Kuratowski's Theorem.
53:23
Štefan Gyürki, Extremal bipartite biregular bi coset graphs
The main goal of the Workshop is to embrace recent results in developing Algebraic Graph T...
published: 30 Nov 2022
Štefan Gyürki, Extremal bipartite biregular bi coset graphs
Štefan Gyürki, Extremal bipartite biregular bi coset graphs
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- published: 30 Nov 2022
- views: 153
The main goal of the Workshop is to embrace recent results in developing Algebraic Graph Theory and its Applications. We are interested in algebraic, spectral and structural characterisation of highly regular graphs, investigating graphs defined on groups, constructing new graphs, codes and designs.
The workshop is organized by Mathematical Center in Akademgorodok in cooperation with the Sino-Russian Mathematics Center at Peking University in Beijing and the Three Gorges Mathematical Research Center at China Three Gorges University in Yichang.
http://mca.nsu.ru/agt7/
Cage (graph theory)
In the mathematical area of graph theory, a cage is a regular graph that has as few vertices as possible for its girth.
Formally, an (r,g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. It is known that an (r,g)-graph exists for any combination of r ≥ 2 and g ≥ 3. An (r,g)-cage is an (r,g)-graph with the fewest possible number of vertices, among all (r,g)-graphs.
If a Moore graph exists with degree r and girth g, it must be a cage. Moreover, the bounds on the sizes of Moore graphs generalize to cages: any cage with odd girth g must have at least
vertices, and any cage with even girth g must have at least
vertices. Any (r,g)-graph with exactly this many vertices is by definition a Moore graph and therefore automatically a cage.
There may exist multiple cages for a given combination of r and g. For instance there are three nonisomorphic (3,10)-cages, each with 70 vertices : the Balaban 10-cage, the Harries graph and the Harries–Wong graph. But there is only one (3,11)-cage : the Balaban 11-cage (with 112 vertices).
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Cage_(graph_theory)
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by Arcana
A Cage
by: ArcanaIn the darkest point of life
When all hopes are gone
What used to be so colorful
Is now grey
At night the sky used to be
So full of stars
What used to be so colorful
Is now grey
It's so hard to get out of this cage
When the outside is so much worse
It's so hard to get rid of these chains
As there's nothing left to fight for