Operations Research Transactions ›› 2024, Vol. 28 ›› Issue (4): 152-161.doi: 10.15960/j.cnki.issn.1007-6093.2024.04.015

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Mixed graphs with negative inertia index 1

Ziyan CHEN1, Yun QIAO1, Yi WANG1,*()   

  1. 1. School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China
  • Received:2022-08-18 Online:2024-12-15 Published:2024-12-20
  • Contact: Yi WANG E-mail:wangy@ahu.edu.cn

Abstract:

A mixed graph is obtained by orienting some edges of a simple graph. The negative inertia index of a mixed graph is defined as the number of negative eigenvalues of its adjacency matrix. This paper mainly studies the negative inertia index of mixed graphs via the second kind Hermitian adjacency matrix. All mixed graphs with negative inertia index 1 are characterized.

Key words: mixed graph, negative inertia index, twin vertices, reduced graph

CLC Number: