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Cores of strongly regular graphs

Importance: High ✭✭✭
Author(s): Cameron, Peter J.
Kazanidis, Priscila A.
Subject: Graph Theory
» Algebraic Graph Theory
Keywords: core
strongly regular
Recomm. for undergrads: no
Posted by: mdevos
on: June 16th, 2008
Question   Does every strongly regular graph have either itself or a complete graph as a core?

If true, this curious question indicates a very interesting property of strongly regular graphs. While on the surface, there would appear to be no particular reason for it to hold, it has already been verified for a number of interesting classes of graphs. Cameron and Kazanidis [CK] showed that it holds for rank-3 graphs, while Godsil and Royle [GR] have showed that it holds for point graphs of generalized quadrangles, block graphs of Steiner systems and orthogonal arrays with sufficiently many points, and for all strongly regular graphs on at most 36 vertices.

Bibliography

*[CK] P. J. Cameron and P. A. Kazanidis, Cores of symmetric graphs, J. Australian Math. Soc., to appear.

[GR] C. Godsil and G.F. Royle, Cores of Geometric Graphs


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Correction

On October 18th, 2011 Anonymous says:

I believe you mean "Godsil and Royle", not "Gordon and Royle".

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