Hoffman–Singleton graph
In the mathematical field of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique strongly regular graph with parameters (50,7,0,1). It was constructed by Alan Hoffman and Robert Singleton while trying to classify all Moore graphs, and is the highest-order Moore graph known to exist. Since it is a Moore graph where each vertex has degree 7, and the girth is 5, it is a (7,5)-cage.
| Hoffman–Singleton graph | |
|---|---|
| Named after | Alan J. Hoffman Robert R. Singleton |
| Vertices | 50 |
| Edges | 175 |
| Radius | 2 |
| Diameter | 2 |
| Girth | 5 |
| Automorphisms | 252,000 (PSU(3,52):2) |
| Chromatic number | 4 |
| Chromatic index | 7 |
| Genus | 29 |
| Properties | Strongly regular Symmetric Hamiltonian Integral Cage Moore graph |
| Table of graphs and parameters | |
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