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

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

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Article number113955
JournalDiscrete Mathematics
Volume347
Issue number6
DOIs
StatePublished - 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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