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A generalization of a theorem of Hoffman
release_5nutfx4bb5ev7gh23ot5azcs5i
by
Jack H. Koolen, Qianqian Yang, Jae Young Yang
Released
as a article
.
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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1612.07085v2
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