{
  "id": "1805.06578",
  "version": "v1",
  "published": "2018-05-17T02:09:05.000Z",
  "updated": "2018-05-17T02:09:05.000Z",
  "title": "On the edge Szeged index of unicyclic graphs with given diameter",
  "authors": [
    "Shengjie He",
    "Rong-Xia Hao",
    "Aimei Yu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The edge Szeged index of a graph $G$ is defined as $Sz_{e}(G)=\\sum\\limits_{uv\\in E(G)}m_{u}(uv|G)m_{v}(uv|G)$, where $m_{u}(uv|G)$ (resp., $m_{v}(uv|G)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp., $u$), respectively. In this paper, we characterize the graph with minimum edge Szeged index among all the unicyclic graphs with given order and diameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-17T02:09:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unicyclic graphs",
      "minimum edge szeged index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}