Herschel graph

In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the graph of a convex polyhedron), and is the smallest polyhedral graph that does not have a Hamiltonian cycle, a cycle passing through all its vertices. The polyhedron whose vertices and edges form this graph is sometimes called the Herschel enneahedron; it is an enneahedron because it has nine faces.

Both the graph and the polyhedron are named after British astronomer Alexander Stewart Herschel, because of Herschel's studies of Hamiltonian cycles in polyhedral graphs (but not of this graph).