What are Regular Graphs? | Graph Theory

What is a regular graph? That is the subject of today's math lesson! A graph is regular if and only if every vertex in the graph has the same degree. If every vertex in a graph has degree r, then we say that graph is "r-regular" or "regular of degree r". If a graph is not regular, as in, it has at least two vertices with distinct degrees, then it is irregular.

Equivalently, a graph is regular if and only if its minimum degree is equal to its maximum degree. The Petersen Graph is an example of a 3-regular graph, and is probably the most well known 3-regular graph. Graphs that are 3-regular are sometimes called "cubic graphs". A complete graph on 5 vertices is 4-regular because every vertex in the graph is adjacent to 4 other vertices, so every vertex has degree 4.

I hope you find this video helpful, and be sure to ask any questions down in the comments!

********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.

********************************************************************

+WRATH OF MATH+

Follow Wrath of Math on...

[leleleleleleticia]

Thanks for this video! Helps me a loooot!

[veradavampire]

omfg i really couldn't get this info anywhere in my lecture notes thank you

[BWY-]

Hi sir how to find the size of a k regular graph

[kage-musha]

then, complete graphs are n-1 regular right ?

[nourmaroun]

In a directed graph when do we talk about a regular graph

[chazy]

Hi sir, sorry for not being active nowadays..and yeah amazing video as always.:-)