Foster cage
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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
The characteristic polynomial of the Foster cage is
