The 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 can be constructed by taking as vertices the unordered pairs from the point set of the Steiner
triple 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 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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References Brouwer, A. E. "Cameron Graph." http://www.win.tue.nl/~aeb/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." http://www.distanceregular.org/graphs/cameron.html . Referenced
on Wolfram|Alpha Cameron Graph
Cite this as:
Weisstein, Eric W. "Cameron Graph." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/CameronGraph.html

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