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Wong graph

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Undirected graph with 30 vertices and 75 edges
Wong graph
Named afterPak-Ken Wong
Vertices30
Edges75
Radius3
Diameter3
Girth5
Automorphisms96
Chromatic number4
Chromatic index5
PropertiesCage
Table of graphs and parameters

In the mathematical field of graph theory, the Wong graph is a 5-regular undirected graph with 30 vertices and 75 edges. 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.

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 . {\displaystyle (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.
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