Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of digraphs with three complementarity eigenvalues   Given a digraph D, the complementarity spectrum of the digraph is defined as
the set of complementarity eigenvalues of its adjacency matrix. This
complementarity spectrum has been shown to be useful in several fields,
particularly in spectral graph theory. The differences between the properties
of the complementarity spectrum for (undirected) graphs and for digraphs, makes
the study of the latter of particular interest, and characterizing strongly
connected digraphs with a small number of complementarity eigenvalues is a non
trivial problem. Recently, strongly connected digraphs with one and two
complementarity eigenvalues have been completely characterized. In this paper
we study strongly connected digraphs with exactly three elements in the
complementarity spectrum, ending with a complete characterization. This leads
to a structural characterization of general digraphs having three
complementarity eigenvalues.

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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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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: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con