In the mathematical field of graph theory, the Foster cage is a 5-regular undirected graph with 30 vertices and 75 edges.[1][2] It is one of the four (5,5)-cage graphs, the others being the Meringer graph, the Robertson–Wegner graph, and the Wong graph.
| Foster cage | |
|---|---|
 | |
| Named after | Ronald Martin Foster |
| Vertices | 30 |
| Edges | 75 |
| Radius | 3 |
| Diameter | 3 |
| Girth | 5 |
| Automorphisms | 30 |
| Chromatic number | 4 |
| Chromatic index | 5 |
| Properties | Cage |
| Table of graphs and parameters | |
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
editThe characteristic polynomial of the Foster cage is
References
edit- ^ Weisstein, Eric W. "Foster Cage". MathWorld.
- ^ 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.