EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 68(82), pp. 46--52 (2000)

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Dominating properties of star complements

Bolian Liu and Peter Rowlinson

Department of Mathematics, Guangdong Normal Polytechnic University, Guangzhou, China and Department of Computing Science and Mathematics, University of Stirling, United Kingdom

Abstract: Let $G$ be a finite graph with an eigenvalue $\mu$ of multiplicity $m$. A set $X$ of $m$ vertices in $G$ is called a {\em star set} for $\mu$ in $G$ if $\mu$ is not an eigenvalue of the {\em star complement} $G-X$. Various dominating properties of the vertices in $G-X$ are established and discussed in the context of memoryless communication networks.

Classification (MSC2000): 05C50; 05C70

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Electronic fulltext finalized on: 1 Nov 2001. This page was last modified: 6 Feb 2002.

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