McLaughlin graph

McLaughlin graph
Vertices 275
Edges 15400
Radius 2
Diameter 2
Girth 3
Automorphisms 1796256000

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

External links

This article is issued from Wikipedia - version of the 4/11/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.