{
  "id": "2311.02792",
  "version": "v1",
  "published": "2023-11-05T23:35:51.000Z",
  "updated": "2023-11-05T23:35:51.000Z",
  "title": "Signed graphs and inverses of their incidence matrices",
  "authors": [
    "Abdullah Alazemi",
    "Milica Andelic",
    "Sudipta Mallik"
  ],
  "comment": "20 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Laplacian matrix $L$ of a signed graph $G$ may or may not be invertible. We present a combinatorial formula of the Moore-Penrose inverse of $L$. This is achieved by finding a combinatorial formula for the Moore-Penrose inverse of an incidence matrix of $G$. This work generalizes related known results on incidence and Laplacian matrices of an unsigned graph. Several examples are provided to show the usefulness of these combinatorial formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-05T23:35:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "15A09"
    ],
    "keywords": [
      "incidence matrix",
      "combinatorial formula",
      "moore-penrose inverse",
      "laplacian matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}