New Bounds for the Laplacian Spectral Radius of a Signed Graph

TL;DR

This paper introduces new bounds for the Laplacian spectral radius of signed graphs that incorporate edge signs, and applies these to derive bounds for unsigned graphs by considering all-positive or all-negative signings.

Contribution

It provides novel bounds for the Laplacian spectral radius of signed graphs that depend on edge signs, extending previous structure-only bounds and applying them to unsigned graphs.

Findings

New bounds depend on edge signs

Bounds improve understanding of spectral properties

Applications to unsigned graphs via edge signing

Abstract

We obtain new bounds for the Laplacian spectral radius of a signed graph. Most of these new bounds have a dependence on edge sign, unlike previously known bounds, which only depend on the underlying structure of the graph. We then use some of these bounds to obtain new bounds for the Laplacian and signless Laplacian spectral radius of an unsigned graph by signing the edges all positive and all negative, respectively.