Signed distance Laplacian matrices for signed graphs

Roshni T. Roy; K. A. Germina; Shahul Hameed K; Thomas Zaslavsky

doi:10.1080/03081087.2022.2158165

Signed distance Laplacian matrices for signed graphs

Roshni T. Roy
, K. A. Germina
, Shahul Hameed K
, Thomas Zaslavsky

Mathematics and Statistics

Binghamton University

Research output: Contribution to journal › Article › peer-review

Abstract

A signed graph is a graph whose edges are labelled either positive or negative. Corresponding to the two signed distance matrices defined for signed graphs, we define two signed distance Laplacian matrices. We characterize singularity and calculate the rank of these matrices and find signed distance Laplacian spectra of some classes of unbalanced signed graphs. We derive most of these results by proving them more generally for weighted signed graphs.

Original language	English
Pages (from-to)	106-117
Number of pages	12
Journal	Linear and Multilinear Algebra
Volume	72
Issue number	1
DOIs	https://doi.org/10.1080/03081087.2022.2158165
State	Published - 2024

Keywords

Signed graph
signed distance Laplacian matrix
signed distance laplacian spectrum
signed distance matrix

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10.1080/03081087.2022.2158165

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title = "Signed distance Laplacian matrices for signed graphs",

abstract = "A signed graph is a graph whose edges are labelled either positive or negative. Corresponding to the two signed distance matrices defined for signed graphs, we define two signed distance Laplacian matrices. We characterize singularity and calculate the rank of these matrices and find signed distance Laplacian spectra of some classes of unbalanced signed graphs. We derive most of these results by proving them more generally for weighted signed graphs.",

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AB - A signed graph is a graph whose edges are labelled either positive or negative. Corresponding to the two signed distance matrices defined for signed graphs, we define two signed distance Laplacian matrices. We characterize singularity and calculate the rank of these matrices and find signed distance Laplacian spectra of some classes of unbalanced signed graphs. We derive most of these results by proving them more generally for weighted signed graphs.

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KW - signed distance Laplacian matrix

KW - signed distance laplacian spectrum

KW - signed distance matrix

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JO - Linear and Multilinear Algebra

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Signed distance Laplacian matrices for signed graphs

Abstract

Keywords

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