{
  "id": "1212.5008",
  "version": "v1",
  "published": "2012-12-20T12:37:49.000Z",
  "updated": "2012-12-20T12:37:49.000Z",
  "title": "On signless Laplacian coefficients of unicyclic graphs with given matching number",
  "authors": [
    "Jie Zhang",
    "Xiao-Dong Zhang"
  ],
  "comment": "39 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be an unicyclic graph of order $n$ and let $Q_G(x)= det(xI-Q(G))={matrix} \\sum_{i=1}^n (-1)^i \\varphi_i x^{n-i}{matrix}$ be the characteristic polynomial of the signless Laplacian matrix of a graph $G$. We give some transformations of $G$ which decrease all signless Laplacian coefficients in the set $\\mathcal{G}(n,m)$. $\\mathcal{G}(n,m)$ denotes all n-vertex unicyclic graphs with matching number $m$. We characterize the graphs which minimize all the signless Laplacian coefficients in the set $\\mathcal{G}(n,m)$ with odd (resp. even) girth. Moreover, we find the extremal graphs which have minimal signless Laplacian coefficients in the set $\\mathcal{G}(n)$ of all $n$-vertex unicyclic graphs with odd (resp. even) girth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-20T12:37:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "matching number",
      "minimal signless laplacian coefficients",
      "n-vertex unicyclic graphs",
      "signless laplacian matrix",
      "extremal graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5008Z"
    }
  }
}