Simple Definition of Petersen Graph | Graph Theory

We introduce the Petersen graph via a combinatorial definition using subsets. This definition of the Petersen graph is easy to understand and useful for proving various results about the graph. #GraphTheory

A Petersen graph's vertices can be labeled by all two element subsets from a five element set. Then, vertices whose subsets are disjoint are adjacent. Vertices whose subsets are not disjoint are not adjacent. With this definition, we'll prove the Petersen graph is 3-regular, or cubic.

Vertex Connectivity of the Petersen Graph:    • Vertex Connectivity of the Petersen G...  

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