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Petersen graph

The Petersen graph is a small graph that serves as a useful example and counterexample in graph theory.

The Petersen graph is the smallest cubic graph that has no Hamiltonian cycle, the smallest cubic graph of girth 5, and the largest cubic graph with diameter 2. It is nonplanar. Although it appears to contain a subgraph homomorphic to K5, it doesn't; however, it does contain a subgraph homomorphic to K3,3.

It is named for the Danish mathematician Julius Petersen.