Work

The signed graphs with symmetric spectra

Year: 2023

Type: preprint

Abstract: It is well known that a graph $G$ has a symmetric spectrum if and only if it is bipartite, a signed graph $Γ=(G,σ)$ has a symmetric spectrum if $G$ is bipartite. However, there exists a spectrally symmetric signed graph $Γ=(G,σ)$ such that $G$ is not bipartite. In this paper, we focus to characterize the signed graphs with symmetric spectra. Some necessary and (or) sufficient conditions for spectrally symmetric signed graphs are given. Moreover, some methods to construct signed graphs with symmetric spectra are found and infinite families of these signed graphs are produced.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2304.06864

Authors: Li, Deqiong, Huang, Qiongxiang

Institutions: Hunan University of Technology and Business, Xinjiang University

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Education Department of Hunan Province, National Natural Science Foundation of China

Awards: G3737008049, G5415449078

OpenAlex ID: W4366197542

Cites:

Cited by: 1

Related to: 10