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21st Cumberland Conference on Graph Theory, Combinatorics, and Computing ---In Honor of Mike Plummer's 70th Birthday
May 15-17, 2008
Vanderbilt University
Nashville, TN, USA

Organizers
Mark Ellingham and Gexin Yu

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Star complements in finite graphs
by
Peter Rowlinson
University of Stirling, Scotland

Let G be a graph with m as an eigenvalue of multiplicity k. A star set for m in G is a set X of k vertices such that m is not an eigenvalue of G-X. The induced subgraph G-X is called a star complement for m in G. Star sets and star complements exist for any eigenvalue of any graph. They can be used to characterize graphs, to find sharp upper bounds for k when m ≠ -1 or 0, and to determine all the graphs with spectra in [-2, ∞).

Date received: April 8, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawn-26.