A generalization of a theorem of Hoffman release_5nutfx4bb5ev7gh23ot5azcs5i

by Jack H. Koolen, Qianqian Yang, Jae Young Yang

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2018  

Abstract

In 1977, Hoffman gave a characterization of graphs with smallest eigenvalue at least -2. In this paper we generalize this result to graphs with smaller smallest eigenvalue. For the proof, we use a combinatorial object named Hoffman graph, introduced by Woo and Neumaier in 1995. Our result says that for every λ≤ -2, if a graph with smallest eigenvalue at least λ satisfies some local conditions, then it is highly structured. We apply our result to graphs which are cospectral with the Hamming graph H(3,q), the Johnson graph J(v, 3) and the 2-clique extension of grids, respectively.
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Type  article
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Date   2018-07-07
Version   v2
Language   en ?
arXiv  1612.07085v2
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