Harries graph

In the mathematical field of graph theory, the Harries graph or Harries -cage is a 3-regular, undirected graph with 70 vertices and 105 edges.
The Harries graph has chromatic number 2, chromatic index 3, radius 6, diameter 6, girth 10 and is Hamiltonian. It is also a 3-vertex-connected and 3-edge-connected, non-planar, cubic graph. It has book thickness 3 and queue number 2.
The characteristic polynomial of the Harries graph is

History

In 1972, A. T. Balaban published a -cage graph, a cubic graph that has as few vertices as possible for girth 10. It was the first -cage discovered but it was not unique.
The complete list of -cage and the proof of minimality was given by O'Keefe and Wong in 1980. There exist three distinct -cage graphs—the Balaban 10-cage, the Harries graph and the Harries–Wong graph. Moreover, the Harries–Wong graph and Harries graph are cospectral graphs.