CentralNotice Petersen graph From Wikipedia, the free encyclopedia Jump to: navigation , search Petersen graph The Petersen graph is most commonly drawn as a pentagon with a pentagram inside, with five spokes. Named after Julius Petersen Vertices 10 Edges 15 Radius 2 Diameter 2 Girth 5 Automorphisms 120 (S 5 ) Chromatic number 3 Chromatic index 4 Fractional chromatic index 3 Properties Cubic Strongly regular Distance-transitive Snark v t e In the mathematical field of graph theory , the Petersen graph is an undirected graph with 10 vertices and 15 edges . It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named for Julius Petersen , who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring. [ 1 ...