The spectral radius of unbalanced signed graphs without negative $C_3$ or $C_4$

TL;DR

This paper characterizes the maximum spectral radius of unbalanced signed graphs that exclude negative 3- and 4-cycles, advancing understanding of spectral properties in signed graph theory.

Contribution

It identifies the signed graphs with the largest spectral radius under specific cycle constraints, a novel result in spectral graph theory.

Findings

Determined the maximum spectral radius for the class of unbalanced signed graphs without negative 3- or 4-cycles.

Characterized the extremal graphs achieving this maximum spectral radius.

Abstract

A signed graph is a graph in which every edge carries a $+$ or a $-$ sign. In this paper, we determine the signed graphs with maximum spectral radius among all unbalanced signed graphs with fixed order that contain neither negative three-cycles nor negative four-cycles.