Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalization of a theorem of Hoffman   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.

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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
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The categories of this paper are: stat
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th