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 K_3,3.

It is named for the Danish mathematician Julius Petersen.