Authors: Cvetković, Dragoš
Rowlinson, Peter
Simić, Slobodan 
Title: Graphs with Least Eigenvalue - 2: The Star Complement Technique
Journal: Journal of Algebraic Combinatorics
Volume: 14
Issue: 1
First page: 5
Last page: 16
Issue Date: 1-Jan-2001
Rank: M21a
ISSN: 0925-9899
DOI: 10.1023/A:1011209801191
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.
Keywords: Eigenspace | Eigenvalue | Graph
Publisher: Springer Link
Project: EPSRC, Grant GR/L94901

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