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.Jessica Wolz, Engineering Linear Layouts with SAT. Master Thesis, University of Tübingen, 2018
The characteristic polynomial of the Harries–Wong graph is
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.A. T. Balaban, A trivalent graph of girth ten, J. Combin. Theory Ser. B 12, 1–5. 1972. It was the first (3-10)-cage discovered but it was not unique.Pisanski, T.; Boben, M.; Marušič, D.; and Orbanić, A. "The Generalized Balaban Configurations." Preprint. 2001. .
The complete list of (3-10)-cages and the proof of minimality was given by O'Keefe and Wong in 1980.M. O'Keefe and P.K. Wong, A smallest graph of girth 10 and valency 3, J. Combin. Theory Ser. B 29 (1980) 91–105. There exist three distinct (3-10)-cage graphs—the Balaban 10-cage, the Harries graph and the Harries–Wong graph.Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 237, 1976. Moreover, the Harries–Wong graph and Harries graph are cospectral graphs.
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