{
  "id": "2312.10012",
  "version": "v1",
  "published": "2023-12-15T18:26:18.000Z",
  "updated": "2023-12-15T18:26:18.000Z",
  "title": "The determinant of the Laplacian matrix of a quaternion unit gain graph",
  "authors": [
    "Ivan I. Kyrchei",
    "Eran Treister",
    "Volodymyr O. Pelykh"
  ],
  "comment": "16 pages, 1 figure",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-15T18:26:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C22",
      "05C50",
      "05C22",
      "05C25",
      "15B33",
      "15B57",
      "15A15"
    ],
    "keywords": [
      "quaternion unit gain graph",
      "laplacian matrix",
      "opposite orientation",
      "combinatorial description",
      "row-column noncommutative determinants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}