You may know it as Kneser graph KG_5,2

The Petersen graph is a symmetrical graph consisting of 10 vertices and 15 edges, with three edges meeting at every vertex. It is commonly drawn as a pentagon surrounding a five-pointed star, with corresponding vertices connected by spokes. Named after Danish mathematician Julius Petersen, the graph is notable because several properties that might be expected of regular graphs fail for it. For example, it has no Hamiltonian cycle and cannot have its edges colored with only three colors. Its small size makes it a useful example and counterexample. It is used in graph theory, combinatorics, and network analysis.