Meringer graph
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| Meringer graph | |
|---|---|
 | |
| Named after | Markus Meringer |
| Vertices | 30 |
| Edges | 75 |
| Radius | 3 |
| Diameter | 3 |
| Girth | 5 |
| Automorphisms | 96 |
| Chromatic number | 3 |
| Chromatic index | 5 |
| Properties | Cage |
| Table of graphs and parameters | |
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.[1][2]
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]\displaystyle{ (x-5) (x-2)^9 x (x+2)^3 (x+3)^2 (x^2+x-4)^3 (x^2+2x-2)^4. }[/math]
References
- ↑ Weisstein, Eric W.. "Meringer Graph". http://mathworld.wolfram.com/MeringerGraph.html.
- ↑ 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.
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