Cameron Graph

The Cameron graph is a strongly regular Hamiltonian graph on 231 vertices with parameters (nu,k,lambda,mu)=(231,30,9,3). It is distance-regular with intersection array {30,20;1,3}, but is not distance-transitive.

It can be constructed by taking as vertices the (22; 2)=231 unordered pairs from the point set of the Steiner triple system S(3,6,22) and joining two vertices when the pairs are disjoint and their union is contained in a block (Brouwer and van Lint 1984).

It has graph spectrum (-3)^(175)9^(55)20^1, and is therefore an integral graph. It has graph automorphism group order Aut(G)=887040.

It is a Hamiltonian graph.

The Cameron graph is implemented in the Wolfram Language as GraphData["CameronGraph"].

See also

Distance-Regular Graph, Distance-Transitive Graph, Strongly Regular Graph

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Brouwer, A. E. "Cameron Graph.", A. E. and van Lint, J. H. "Strongly Regular Graphs and Partial Geometries." In Enumeration and Design: Papers from the conference on combinatorics held at the University of Waterloo, Waterloo, Ont., June 14-July 2, 1982 (Ed. D. M. Jackson and S. A. Vanstone). Toronto, Canada: Academic Press, pp. 85-122, 1984.Brouwer, A. E. and van Maldeghem, H. "The Cameron Graph." §10.54 in Strongly Regular Graphs. Cambridge, England: Cambridge University Press, pp. 332-333, 2022.Cameron, P. J.; Goethals, J.-M.; and Seidel, J. J. "Strongly Regular Graphs having Strongly Regular Subconstituents." J. Alg. 55, 257-280, "Cameron Graph."

Referenced on Wolfram|Alpha

Cameron Graph

Cite this as:

Weisstein, Eric W. "Cameron Graph." From MathWorld--A Wolfram Web Resource.

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