Wong graph

Wong graph
Named after	Pak-Ken Wong
Vertices	30
Edges	75
Radius	3
Diameter	3
Girth	5
Automorphisms	96
Chromatic number	4
Chromatic index	5
Properties	Cage

In the mathematical field of graph theory, the Wong graph is a 5-regular undirected graph with 30 vertices and 75 edges.^[1][2] It is one of the four (5,5)-cage graphs, the others being the Foster cage, the Meringer graph, and the Robertson–Wegner graph.

Like the unrelated Harries–Wong graph, it is named after Pak-Ken Wong.^[3]

It has chromatic number 4, diameter 3, and is 5-vertex-connected.

Algebraic properties

The characteristic polynomial of the Wong graph is

$(x-5)(x+1)^2(x^2-5)^3(x-1)^5(x^2+x-5)^8.$

References

1. Weisstein, Eric W., "Wong Graph", MathWorld.
2. Meringer, Markus (1999), "Fast generation of regular graphs and construction of cages", Journal of Graph Theory 30 (2): 137–146, doi:10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G, MR 1665972.
3. Wong, P. K. "Cages--A Survey." J. Graph Th. 6, 1-22, 1982.