Abstract
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.
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Cvetković, D., Rowlinson, P. & Simić, S. Graphs with Least Eigenvalue −2: The Star Complement Technique. Journal of Algebraic Combinatorics 14, 5–16 (2001). https://doi.org/10.1023/A:1011209801191
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DOI: https://doi.org/10.1023/A:1011209801191