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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: Graph Theory playlist: Graph Theory exercises: ◉Textbooks I Like◉ Graph Theory: Real Analysis: Proofs and Set Theory: (available for free online) Statistics:
