Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Products and Line Graphs of Signed Graphs, their Eigenvalues and
  Energy   In this article we examine the adjacency and Laplacian matrices and their
eigenvalues and energies of the general product (non-complete extended $p$-sum,
or NEPS) of signed graphs. We express the adjacency matrix of the product in
terms of the Kronecker matrix product and the eigenvalues and energy of the
product in terms of those of the factor signed graphs. For the Cartesian
product we characterize balance and compute expressions for the Laplacian
eigenvalues and Laplacian energy. We give exact results for those signed
planar, cylindrical and toroidal grids which are Cartesian products of signed
paths and cycles.
  We also treat the eigenvalues and energy of the line graphs of signed graphs,
and the Laplacian eigenvalues and Laplacian energy in the regular case, with
application to the line graphs of signed grids that are Cartesian products and
to the line graphs of all-positive and all-negative complete graphs.

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The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc