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

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

Published 2023-12-15Version 1

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.