A generalization of a theorem of Hoffman [article]

Jack H. Koolen, Qianqian Yang, Jae Young Yang
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
more » ... H(3,q), the Johnson graph J(v, 3) and the 2-clique extension of grids, respectively.
arXiv:1612.07085v2 fatcat:5nutfx4bb5ev7gh23ot5azcs5i