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The 231-Cameron graph is a strongly regular Hamiltonian graph on 231 vertices with parameters . It is distance-regular with intersection array , but is not distance-transitive. It is named after mathematician Peter J. Cameron (Cameron et al. 1978).

It can be constructed by taking as vertices the unordered pairs from the point set of the Steiner system 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 , and is therefore an integral graph. It has graph automorphism group order .

It is a Hamiltonian graph.

The 231-Cameron graph is implemented in the Wolfram Language as GraphData["CameronGraph"]. It should not be confused with the Cameron cubic Hamiltonian graphs constructed by Kathleen Cameron, or with the Cameron-Montanaro-Newman-Severini-Winter graph, an 18-vertex graph related to the quantum chromatic number.

See also

Cameron Cubic Hamiltonian Graphs, Cameron-Montanaro-Newman-Severini-Winter Graph, Distance-Regular Graph, Distance-Transitive Graph, Strongly Regular Graph

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References

Brouwer, A. E. "Cameron Graph." https://aeb.win.tue.nl/drg/graphs/Cameron.html.Brouwer, 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, 1978.DistanceRegular.org. "Cameron Graph." https://www.math.mun.ca/distanceregular/graphs/cameron.html.

Referenced on Wolfram|Alpha

Cameron Graph

Cite this as:

Weisstein, Eric W. "Cameron Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CameronGraph.html

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