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ON THE MULTIPLICITIES OF GRAPH EIGENVALUES

Published online by Cambridge University Press:  12 May 2003

F. K. BELL  and
P. ROWLINSON
F. K. BELL
Affiliation:
Mathematics and Statistics Group Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA f.k.bell@stir.ac.uk
P. ROWLINSON
Affiliation:
Mathematics and Statistics Group Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA p.rowlinson@stir.ac.uk
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Abstract

Star complements and associated quadratic functions are used to obtain a sharp upper bound for the order of a graph with an eigenspace of prescribed codimension. It is shown that for regular graphs the bound can be reduced by 1, and that this reduced bound is attained by a regular graph $G$ if and only if $G$ is an extremal strongly regular graph.

Keywords

05C50
Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 3 , May 2003 , pp. 401 - 408
Copyright
© The London Mathematical Society 2003

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