Simple Definition of Petersen Graph | Graph Theory

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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.

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I just ran across the Petersen graph yesterday when tutoring someone in discrete math, and the problem was rather tricky. Thanks for sharing your knowledge about graph theory so we all can learn!

PunmasterSTP
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can you also tell us about the isomorphism of Peterson graph

raginibhayana
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Thank you - the amazing famous pathological counter-example in graph theory!!! - your shtick!

theproofessayist
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Greetings, could you make a video explaining Ramsey numbers?

DrJimmable
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Hello, can I please ask you a question on subsets? how many subsets of {1, 2, 3, …, 20} are there with no more than 2 consecutive integers? Can you please explain step by step how to arrive at the answer?

zacksnyder