McLaughlin graph
Page Module:Message box/ambox.css has no content.
This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (November 2023) |
Page Module:Message box/ambox.css has no content.
This article relies largely or entirely on a single source. (April 2024) |
Page Template:Infobox graph/styles.css has no content.Page Module:Infobox/styles.css has no content.
| McLaughlin graph | |
|---|---|
| Vertices | 275 |
| Edges | 15400 |
| Radius | 2 |
| Diameter | 2 |
| Girth | 3 |
| Automorphisms | 1796256000 |
| Table of graphs and parameters | |
In the mathematical field of graph theory, the McLaughlin graph is a strongly regular graph with parameters (275, 112, 30, 56) and is the only such graph.
The group theorist Jack McLaughlin discovered that the automorphism group of this graph had a subgroup of index 2 which was a previously undiscovered finite simple group, now called the McLaughlin sporadic group.
The automorphism group has rank 3, meaning that its point stabilizer subgroup divides the remaining 274 vertices into two orbits. Those orbits contain 112 and 162 vertices. The former is the colinearity graph of the generalized quadrangle GQ(3,9). The latter is a strongly regular graph called the local McLaughlin graph.
References
- Page Module:Citation/CS1/styles.css has no content.McLaughlin, Jack (1969), "A simple group of order 898,128,000", in Brauer, R.; Sah, Chih-han (eds.), Theory of Finite Groups (Symposium, Harvard Univ., Cambridge, Mass., 1968), Benjamin, New York, pp. 109–111, MR 0242941
External links
- Page Module:Citation/CS1/styles.css has no content.Andries Brouwer. "McLaughlin graph".
