Goldner–Harary graph

Goldner–Harary graph
Named afterA. Goldner,
Frank Harary
Vertices11
Edges27
Radius2
Diameter2
Girth3
Automorphisms12 (D6)
Chromatic number4
Chromatic index8
PropertiesPolyhedral
Planar
Chordal
Perfect
Treewidth 3
Table of graphs and parameters

In the mathematical field of graph theory, the Goldner–Harary graph is a simple undirected graph with 11 vertices and 27 edges. It is named after Anita M. Goldner and Frank Harary, who proved in 1975 that it was the smallest non-Hamiltonian maximal planar graph. The same graph had already been given as an example of a non-Hamiltonian simplicial polyhedron by Branko Grünbaum in 1967.