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...
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
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"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
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