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Graphs with least eigenvalue - 2: The star complement technique

Cvetkovic D, Rowlinson P & Simic S (2001) Graphs with least eigenvalue - 2: The star complement technique. Journal of Algebraic Combinatorics, 14 (1), pp. 5-16.

Let G be a connected graph with least eigenvalue -2, of multiplicity k. A star complement for -2 in G is an induced subgraph H = G - X such that |X| = k and -2 is not an eigenvalue of H. In the case that G is a generalized line graph, a characterization of such subgraphs is used to decribe the eigenspace of -2. In some instances, G itself can be characterized by a star complement. If G is not a generalized line graph, G is an exceptional graph, and in this case it is shown how a star complement can be used to construct G without recourse to root systems.

graph; eigenvalue; eigenspace

Journal of Algebraic Combinatorics: Volume 14, Issue 1

Author(s)Cvetkovic, Dragos; Rowlinson, Peter; Simic, Slobodan
Publication date31/07/2001
PublisherKluwer Academic Publishers
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