On the inertia index of a mixed graph with the matching number

2019/09/16 by Shengjie He, Rong‐Xia Hao, He, Shengjie +3
Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1909.07146

openalex publication_date 2019/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A mixed graph \widetildeG is obtained by orienting some edges of G, where G is the underlying graph of \widetildeG. The positive inertia index, denoted by p⁺(G), and the negative inertia index, denoted by n^-(G), of a mixed graph \widetildeG are the integers specifying the numbers of positive and negative eigenvalues of the Hermitian adjacent matrix of \widetildeG, respectively. In this paper, we study the positive and negative inertia index of the mixed unicyclic graph. Moreover, we give the upper and lower bounds of the positive and negative inertia index of the mixed graph, and characterize the mixed graphs which attain the upper and lower bounds respectively.

Related

• Mixed graphs with cut vertices having exactly two positive eigenvalues
• On graphs with exactly two positive eigenvalues
• The relationship between the negative inertia index of graph G and its girth g and diameter d
• The inertia of weighted unicyclic graphs
• Connected signed graphs with given inertia indices and given girth