| Harries - Wong graph | |
| Namesake: | W. Harries, Pak-Ken Wong |
| Vertices: | 70 |
| Edges: | 105 |
| Automorphisms: | 24 (S4) |
| Girth: | 10 |
| Genus: | 9 |
| Diameter: | 6 |
| Radius: | 6 |
| Chromatic Number: | 2 |
| Chromatic Index: | 3 |
| Properties: | Cubic Cage Triangle-free Hamiltonian |
| Book Thickness: | 3 |
| Queue Number: | 2 |
In the mathematical field of graph theory, the Harries - Wong graph is a 3-regular undirected graph with 70 vertices and 105 edges.
The Harries - Wong 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.[1]
The characteristic polynomial of the Harries–Wong graph is
(x-3)(x-1)4(x+1)4(x+3)(x2-6)(x2-2)(x4-6x2+2)5(x4-6x2+3)4(x4-6x2+6)5.
In 1972, A. T. Balaban published a (3-10)-cage graph, a cubic graph that has as few vertices as possible for girth 10.[2] It was the first (3-10)-cage discovered but it was not unique.[3]
The complete list of (3-10)-cages and the proof of minimality was given by O'Keefe and Wong in 1980.[4] There exist three distinct (3-10)-cage graphs—the Balaban 10-cage, the Harries graph and the Harries - Wong graph.[5] Moreover, the Harries - Wong graph and Harries graph are cospectral graphs.