{{Short description|Graph with 30 vertices and 75 edges}} {{Context|date=April 2021}} {{infobox graph | name = Meringer graph | namesake = Markus Meringer | vertices = 30 | edges = 75 | automorphisms = 96 | girth = 5 | diameter = 3 | radius = 3 | chromatic_number = 3 | chromatic_index = 5 | properties = Cage |image=Meringer graph.svg}} In the mathematical field of graph theory, the '''Meringer graph''' is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer.<ref>{{MathWorld|urlname=MeringerGraph|title=Meringer 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 Robertson–Wegner graph, and the Wong graph.
It has chromatic number 3, diameter 3, and is 5-vertex-connected.
==Algebraic properties== The characteristic polynomial of the Meringer graph is
: <math>(x-5) (x-2)^9 x (x+2)^3 (x+3)^2 (x^2+x-4)^3 (x^2+2x-2)^4.</math>
== References == {{reflist}}
Category:Individual graphs Category:Regular graphs