# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

Z. Stanić

Title:

Some properties of the eigenvalues of the net Laplacian matrix of a signed graph

Source:

Discussiones Mathematicae Graph Theory

Received: 2019-09-30, Revised: 2020-03-10, Accepted: 2020-03-10, https://doi.org/10.7151/dmgt.2314

Abstract:

Given a signed graph $\dot{G}$, let $A_{\dot{G}}$ and $D^{\pm}_{\dot{G}}$ denote its standard adjacency matrix and the diagonal matrix of vertex net-degrees, respectively. The net Laplacian matrix of $\dot{G}$ is defined to be $N_{\dot{G}}=D^{\pm}_{\dot{G}}-A_{\dot{G}}$. In this study we give some properties of the eigenvalues of $N_{\dot{G}}$. In particular, we consider their behaviour under some edge perturbations, establish some relations between them and the eigenvalues of the standard Laplacian matrix and give some lower and upper bounds for the largest eigenvalue of $N_{\dot{G}}$.

Keywords:

(net) Laplacian matrix, edge perturbations, largest eigenvalue, net-degree