{
  "id": "1904.04131",
  "version": "v1",
  "published": "2019-04-08T15:40:40.000Z",
  "updated": "2019-04-08T15:40:40.000Z",
  "title": "Computing the Mostar index in networks with applications to molecular graphs",
  "authors": [
    "Niko Tratnik"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Recently, a bond-additive topological descriptor, named as the Mostar index, has been introduced as a measure of peripherality in networks. For a connected graph $G$, the Mostar index is defined as $Mo(G) = \\sum_{e=uv \\in E(G)} |n_u(e) - n_v(e)|$, where for an edge $e=uv$ we denote by $n_u(e)$ the number of vertices of $G$ that are closer to $u$ than to $v$ and by $n_v(e)$ the number of vertices of $G$ that are closer to $v$ than to $u$. In this paper, we generalize the definition of the Mostar index to weighted graphs and prove that the Mostar index of a weighted graph can be computed in terms of Mostar indices of weighted quotient graphs. As a consequence, we show that the Mostar index of a benzenoid system can be computed in sub-linear time with respect to the number of vertices. Finally, our method is applied to some benzenoid systems and to a fullerene patch.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-08T15:40:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "92E10",
      "05C12",
      "05C22",
      "05C82"
    ],
    "keywords": [
      "mostar index",
      "molecular graphs",
      "applications",
      "benzenoid system",
      "weighted graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}