Characterizing the mixed graphs with exactly one positive eigenvalue and its application to mixed graphs determined by their H-spectra

Bo-Jun Yuan, Yi Wang and Jing Xu

Applied Mathematics and Computation, 2020, vol. 380, issue C

Abstract: A mixed graph is obtained by orienting some edges of a simple graph. The positive inertia index of a mixed graph is defined as the number of positive eigenvalues of its Hermitian adjacency matrix, including multiplicities. In this paper, we study the positive inertia indices of mixed graphs. Our main results provide a characterization of mixed graphs with positive inertia index 1. As an application, some classes of mixed graphs determined by their H-spectra are fixed.

Keywords: Inertia index; Mixed graph; DHS; Hermitian adjacency matrix (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:380:y:2020:i:c:s0096300320302484

DOI: 10.1016/j.amc.2020.125279

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