Authors: Cvetković, Dragoš
Rowlinson, Peter
Simić, Slobodan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Star complements and exceptional graphs
Journal: Linear Algebra and Its Applications
Volume: 423
Issue: 1
First page: 146
Last page: 154
Issue Date: 1-May-2007
Rank: M22
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.01.008
Let G be a finite graph of order n with an eigenvalue μ of multiplicity k. (Thus the μ-eigenspace of a (0, 1)-adjacency matrix of G has dimension k.) A star complement for μ in G is an induced subgraph G - X of G such that | X | = k and G - X does not have μ 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.
Keywords: Eigenvalue | Graph | Star complement
Publisher: Elsevier
Project: EPSRC, Grant EP/D010748/1

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