The determinant of the Laplacian matrix of a quaternion unit gain graph

Ivan I. Kyrchei; Eran Treister; Volodymyr O. Pelykh

doi:https://doi.org/10.1016/j.disc.2024.113955

The determinant of the Laplacian matrix of a quaternion unit gain graph

Ivan I. Kyrchei, Eran Treister, Volodymyr O. Pelykh

Department of Computer Science

Ben-Gurion University of the Negev

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

Abstract

A quaternion unit gain graph is a graph where each orientation of an edge is given a quaternion unit, and the opposite orientation is assigned the inverse of this quaternion unit. In this paper, we provide a combinatorial description of the determinant of the Laplacian matrix of a quaternion unit gain graph by using row-column noncommutative determinants recently introduced by one of the authors. A numerical example is presented for illustrating our results.

Original language	American English
Article number	113955
Journal	Discrete Mathematics
Volume	347
Issue number	6
DOIs	https://doi.org/10.1016/j.disc.2024.113955
State	Published - 1 Jun 2024

Keywords

Gain graph
Incidence matrix
Laplacian matrix
Noncommutative determinant
Quaternion matrix

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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https://doi.org/10.1016/j.disc.2024.113955

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AB - A quaternion unit gain graph is a graph where each orientation of an edge is given a quaternion unit, and the opposite orientation is assigned the inverse of this quaternion unit. In this paper, we provide a combinatorial description of the determinant of the Laplacian matrix of a quaternion unit gain graph by using row-column noncommutative determinants recently introduced by one of the authors. A numerical example is presented for illustrating our results.

KW - Gain graph

KW - Incidence matrix

KW - Laplacian matrix

KW - Noncommutative determinant

KW - Quaternion matrix

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The determinant of the Laplacian matrix of a quaternion unit gain graph

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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