Geodesic
Graphs with least eigenvalue $-2$: The star complement technique
Journal of Algebraic Combinatorics, Tome 14 (2001) no. 1, pp. 5-16.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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: graph, eigenvalue, eigenspace 
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     title = {Graphs with least eigenvalue $-2$: {The} star complement technique},
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Cvetković, D.; Rowlinson, P.; Simić, S.K. Graphs with least eigenvalue $-2$: The star complement technique. Journal of Algebraic Combinatorics, Tome 14 (2001) no. 1, pp. 5-16. http://geodesic.mathdoc.fr/item/JAC_2001__14_1_a5/