EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)
Vol. 76(90), pp. 25–30 (2004)

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STAR COMPLEMENTS AND MAXIMAL EXCEPTIONAL GRAPHS

P. Rowlinson

Mathematics and Statistics Group, Department of Computing Science and Mathematics, University of Stirling, Scotland, FK9 4LA

Abstract: If $G$ is a maximal exceptional graph then either (a) $G$ is the cone over a graph switching-equivalent to the line graph $L(K_8)$ or (b) $G$ has $K_8$ as a star complement for the eigenvalue $-2$ (or both). In case (b) it is shown how $G$ can be constructed from $K_8$ using intersecting families of $3$-sets.

Keywords: exceptional graph, eigenvalue; star complement

Classification (MSC2000): 05C50

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Electronic fulltext finalized on: 17 Dec 2004. This page was last modified: 9 Feb 2005.

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