{{infobox graph | name = Foster cage | image = 170px | namesake = Ronald Martin Foster | vertices = 30 | edges = 75 | automorphisms = 30 | girth = 5 | diameter = 3 | radius = 3 | chromatic_number = 4 | chromatic_index = 5 | properties = Cage }} In the mathematical field of graph theory, the '''Foster cage''' is a 5-regular undirected graph with 30 vertices and 75 edges.<ref>{{MathWorld|urlname=FosterCage|title=Foster Cage}}</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 Meringer graph, the Robertson–Wegner graph, and the Wong graph.
Like the unrelated Foster graph, it is named after R. M. Foster.
It has chromatic number 4, diameter 3, and is 5-vertex-connected.
==Algebraic properties== The characteristic polynomial of the Foster cage is
: <math>(x-5)(x+1)(x^2-5)^2(x^2+2x-4)^2(x-2)^4(x^4+2x^3-6x^2-7x+11)^4.</math>
== References == {{reflist}}
Category:Individual graphs Category:Regular graphs