DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

Journal Impact Factor (JIF 2023): 0.5

5-year Journal Impact Factor (2023): 0.6

CiteScore (2023): 2.2

SNIP (2023): 0.681

Discussiones Mathematicae Graph Theory

Article in volume

Authors:

Z. Stanić

Zoran Stanić

University of Belgrade

email: zstanic@matf.bg.ac.rs

Title:

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

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Source:

Discussiones Mathematicae Graph Theory 42(3) (2022) 893-903

Received: 2019-09-30 , Revised: 2020-03-10 , Accepted: 2020-03-10 , Available online: 2020-03-18 , 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

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