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A generalization of a theorem of Hoffman
[article]
2018
arXiv
pre-print
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
arXiv:1612.07085v2
fatcat:5nutfx4bb5ev7gh23ot5azcs5i