Matrices in the Theory of Signed Simple Graphs

TL;DR

This paper reviews the use of various matrices such as adjacency, incidence, and Laplacian matrices in the study of signed simple graphs, highlighting their roles in understanding graph properties.

Contribution

It synthesizes existing research on matrices associated with signed graphs, emphasizing their applications in analyzing graph structure and regularity.

Findings

Summarizes key matrix types used in signed graph theory

Highlights the importance of Laplacian and adjacency matrices

Connects matrix properties to graph regularity

Abstract

I discuss the work of many authors on various matrices used to study signed graphs, concentrating on adjacency and incidence matrices and the closely related topics of Kirchhoff (`Laplacian') matrices, line graphs, and very strong regularity.