New matrices for the spectral theory of mixed graphs, Part II

TL;DR

This paper extends spectral graph theory for mixed graphs by introducing new integrated matrices and analyzing their spectral properties in relation to graph structure.

Contribution

It introduces the integrated Laplacian, signless Laplacian, and normalized Laplacian matrices for mixed graphs, expanding the spectral analysis framework.

Findings

Spectral properties of new matrices relate to graph structure

Extended spectral analysis tools for mixed graphs

Deeper understanding of mixed graph characteristics

Abstract

The concept of the integrated adjacency matrix for mixed graphs was first introduced in [9], where its spectral properties were analyzed in relation to the structural characteristics of the mixed graph. Building upon this foundation, this paper introduces the integrated Laplacian matrix, the integrated signless Laplacian matrix, and the normalized integrated Laplacian matrix for mixed graphs. We further explore how the spectra of these matrices relate to the structural properties of the mixed graph.