Relations between the inertia indices of a mixed graph and those of its underlying graph

Mixed graphs with cut vertices having exactly two positive eigenvalues

“…Clearly, the Hermitian adjacency matrix of a mixed graph is a natural generalization of the adjacency matrix of a simple graph. Therefore the mixed graph attracts more and more researchers' attention; see [13,21,24,25,28,35,36,52,51,50,59,60].…”

“…Zheng et al [63] gave some eigenvalue inequalities between two mixed graphs by means of inertia indices. Wei et al [51] investigated relations between the inertia indices of a mixed graph and those of its underlying graph. Yuan et al [60] provided a characterization of mixed graphs with positive inertia index 1 and studied the determination of some mixed graphs by their H-spectra.…”

“…Motivated by the results in [13,28,35,51,52,49,50,56,57,60], in this paper, we consider the mixed graphs with connected underlying graph and characterize all mixed graphs with cut vertices which have positive inertia index 2. For more general setting, we leave it for further research.…”