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!

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