{
  "id": "1912.09604",
  "version": "v1",
  "published": "2019-12-20T01:22:04.000Z",
  "updated": "2019-12-20T01:22:04.000Z",
  "title": "The determinant of the distance matrix of graphs with at most two cycles",
  "authors": [
    "Ezequiel Dratman",
    "Luciano N. Grippo",
    "Matín D. Safe",
    "Celso M. da Silva Jr.",
    "Renata R. Del-Vecchio"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a connected graph on $n$ vertices and $D(G)$ its distance matrix. The formula for computing the determinant of this matrix in terms of the number of vertices is known when the graph is either a tree or {a} unicyclic graph. In this work we generalize these results, obtaining the determinant of the distance matrix for {all graphs} in a {class, including trees, unicyclic and bicyclic graphs. This class actually includes graphs with many cycles, provided that each block of the graph is at most bicyclic.}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-20T01:22:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "G.2.1",
      "G.2.1"
    ],
    "keywords": [
      "distance matrix",
      "determinant",
      "unicyclic graph",
      "bicyclic graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}