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- W2565561754 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 $lambda leq -2$, if a graph with smallest eigenvalue at least $lambda$ 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." @default.
- W2565561754 created "2017-01-06" @default.
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- W2565561754 date "2016-12-21" @default.
- W2565561754 modified "2023-09-27" @default.
- W2565561754 title "A generalization of a theorem of Hoffman" @default.
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