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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Star complements and exceptional graphs
Author(s): Cvetkovic, Dragos
Rowlinson, Peter
Simic, Slobodan K
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Keywords: Graph
Star complement
Issue Date: May-2007
Date Deposited: 28-Jan-2014
Citation: Cvetkovic D, Rowlinson P & Simic SK (2007) Star complements and exceptional graphs. Linear Algebra and Its Applications, 423 (1), pp. 146-154.
Abstract: Let G be a finite graph of order n with an eigenvalue ? of multiplicity k. (Thus the ?-eigenspace of a (0,1)-adjacency matrix of G has dimension k.) A star complement for ? in G is an induced subgraph G-X of G such that |X|=k and G-X does not have ? as an eigenvalue. An exceptional graph is a connected graph, other than a generalized line graph, whose eigenvalues lie in [-2,?). We establish some properties of star complements, and of eigenvectors, of exceptional graphs with least eigenvalue -2.
DOI Link: 10.1016/j.laa.2007.01.008
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