{
  "id": "1209.3455",
  "version": "v1",
  "published": "2012-09-16T01:55:21.000Z",
  "updated": "2012-09-16T01:55:21.000Z",
  "title": "On the spectral moment of graphs with given clique number",
  "authors": [
    "Shuna Hu",
    "Shuchao Li",
    "Xixi Zhang"
  ],
  "comment": "12 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathscr{L}_{n,t}$ be the set of all $n$-vertex connected graphs with clique number $t$\\,($2\\leq t\\leq n)$. For $n$-vertex connected graphs with given clique number, lexicographic ordering by spectral moments ($S$-order) is discussed in this paper. The first $\\sum_{i=1}^{\\lfloor\\frac{n-t-1}{3}\\rfloor}(n-t-3i)+1$ graphs with $3\\le t\\le n-4$, and the last few graphs, in the $S$-order, among $\\mathscr{L}_{n,t}$ are characterized. In addition, all graphs in $\\mathscr{L}_{n,n}\\bigcup\\mathscr{L}_{n,n-1}$ have an $S$-order; for the cases $t=n-2$ and $t=n-3$ the first three and the first seven graphs in the set $\\mathscr{L}_{n,t}$ are characterized, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-16T01:55:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "clique number",
      "spectral moment",
      "vertex connected graphs",
      "first seven graphs",
      "lexicographic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.3455H"
    }
  }
}