{
  "id": "1809.01901",
  "version": "v1",
  "published": "2018-09-06T09:31:52.000Z",
  "updated": "2018-09-06T09:31:52.000Z",
  "title": "Extremal graphs for vertex-degree-based invariants with given degree sequences",
  "authors": [
    "Muhuo Liu",
    "Kexiang Xu",
    "Xiao-Dong Zhang"
  ],
  "comment": "23 pages",
  "journal": "Discrete Applied Mathematics, 2018",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a symmetric bivariable function $f(x,y)$, let the {\\it connectivity function} of a connected graph $G$ be $M_f(G)=\\sum_{uv\\in E(G)}f(d(u),d(v))$, where $d(u)$ is the degree of vertex $u$. In this paper, we prove that for an escalating (de-escalating) function $f(x,y)$, there exists a BFS-graph with the maximum (minimum) connectivity function $M_f(G)$ among all graphs with a $c-$cyclic degree sequence $\\pi=(d_1,d_2, \\ldots, d_n)$ and $d_n=1$, and obtain the majorization theorem for connectivity function for unicyclic and bicyclic degree sequences. Moreover, some applications of graph invariants based on degree are included.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-06T09:31:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12",
      "05C35"
    ],
    "keywords": [
      "extremal graphs",
      "vertex-degree-based invariants",
      "connectivity function",
      "bicyclic degree sequences",
      "symmetric bivariable function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}