Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Construction of Upper and Lower Bounds for the HOMO-LUMO Spectral Gap   In this paper we study spectral properties of graphs which are constructed
from two given invertible graphs by bridging them over a bipartite graph. We
analyze the so-called HOMO-LUMO spectral gap which is the difference between
the smallest positive and largest negative eigenvalue of the adjacency matrix
of a graph. We investigate its dependence on the bridging bipartite graph and
we construct a mixed integer semidefinite program for maximization of the
HOMO-LUMO gap with respect to the bridging bipartite graph. We also derive
upper and lower bounds for the optimal HOMO-LUMO spectral graph by means of
semidefinite relaxation techniques. Several computational examples are also
presented in this paper.

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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: econ