The Hoffman-Singleton Graph
The Hoffman-Singleton graph. Source.
The Hoffman-Singleton graph is a strongly regular (50,7,0,1)-graph.
In numbers:
| #vertices | ||
| degree | ||
| girth | ||
| diameter | ||
| valency |
Construction of the graph
The six totals: the edge-colorings of K6 with five colors
| color | ∞ | 0 | 1 | 2 | 3 | 4 |
| r | AB CF DE | AB DE CF | AB FD CE | AB DC FE | AB FE DC | AB EC DF |
| o | AC DB EF | AC FD EB | AC EF DB | AC BE DF | AC ED BF | AC BF ED |
| y | AD EC FB | AD CB FE | AD BE FC | AD FB EC | AD CF EB | AD FE CB |
| i | AE FD BC | AE BF DC | AE DC BF | AE CF BD | AE BC FD | AE DB FC |
| v | AF BE CD | AF EC BD | AF CB ED | AF ED CB | AF DB CE | AF CD BE |