Signed Distance Laplacian Matrices for Signed Graphs

TL;DR

This paper introduces signed distance Laplacian matrices for signed graphs, characterizes graph balance using these matrices, and computes their spectra for certain unbalanced graphs, advancing spectral graph theory.

Contribution

It defines two new signed distance Laplacian matrices and explores their spectral properties, providing tools to analyze balance in signed graphs.

Findings

Characterization of balance in signed graphs using the new matrices

Spectral analysis of unbalanced signed graphs

Introduction of two signed distance Laplacian matrices

Abstract

A signed graph is a graph whose edges are labeled either positive or negative. Corresponding to the two signed distance matrices defined for signed graphs, we define two signed distance laplacian matrices. We characterize balance in signed graphs using these matrices and find signed distance laplacian spectra of some classes of unbalanced signed graphs.