Wong graph

{{Short description|Undirected graph with 30 vertices and 75 edges}} {{infobox graph | name = Wong graph | namesake = Pak-Ken Wong | vertices = 30 | edges = 75 | automorphisms = 96 | girth = 5 | diameter = 3 | radius = 3 | chromatic_number = 4 | chromatic_index = 5 | properties = Cage |image=Wong graph.svg}} In the mathematical field of graph theory, the '''Wong graph''' is a 5-regular undirected graph with 30 vertices and 75 edges.<ref>{{MathWorld|urlname=WongGraph|title=Wong Graph}}</ref><ref>{{citation | last = Meringer | first = Markus | doi = 10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G | issue = 2 | journal = Journal of Graph Theory | mr = 1665972 | pages = 137–146 | title = Fast generation of regular graphs and construction of cages | volume = 30 | year = 1999}}.</ref> 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.<ref>Wong, P. K. "Cages--A Survey." J. Graph Th. 6, 1-22, 1982.</ref>

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

==Algebraic properties== The characteristic polynomial of the Wong graph is : <math>(x-5)(x+1)^2(x^2-5)^3(x-1)^5(x^2+x-5)^8.</math>

== References == {{reflist}}

Category:Individual graphs Category:Regular graphs