Star complements and exceptional graphs
نویسندگان
چکیده
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. © 2007 Elsevier Inc. All rights reserved. AMS classification: 05C50
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