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Harries–Wong graph

From Wikipedia, the free encyclopedia

Harries–Wong graph
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In the mathematical field of graph theory, the HarriesWong graph is a 3-regular undirected graph with 70 vertices and 105 edges.[1]

Quick Facts –Wong graph, Named after ...

The HarriesWong 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.[2]

The characteristic polynomial of the Harries–Wong graph is

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History

In 1972, A. T. Balaban published a (3-10)-cage graph, a cubic graph that has as few vertices as possible for girth 10.[3] It was the first (3-10)-cage discovered but it was not unique.[4]

The complete list of (3-10)-cages and the proof of minimality was given by O'Keefe and Wong in 1980.[5] There exist three distinct (3-10)-cage graphs—the Balaban 10-cage, the Harries graph and the HarriesWong graph.[6] Moreover, the HarriesWong graph and Harries graph are cospectral graphs.

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References

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