{
  "id": "2108.03895",
  "version": "v1",
  "published": "2021-08-09T09:24:45.000Z",
  "updated": "2021-08-09T09:24:45.000Z",
  "title": "The signless Laplacian spectral radius of graphs without intersecting odd cycles",
  "authors": [
    "Ming-Zhu Chen",
    "A-Ming Liu",
    "Xiao-Dong Zhang"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $F_{a_1,\\dots,a_k}$ be a graph consisting of $k$ cycles of odd length $2a_1+1,\\dots, 2a_k+1$, respectively which intersect in exactly a common vertex, where $k\\geq1$ and $a_1\\ge a_2\\ge \\cdots\\ge a_k\\ge 1$. In this paper, we present a sharp upper bound for the signless Laplacian spectral radius of all $F_{a_1,\\dots,a_k}$-free graphs and characterize all extremal graphs which attain the bound. The stability methods and structure of graphs associated with the eigenvalue are adapted for the proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-09T09:24:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C35"
    ],
    "keywords": [
      "signless laplacian spectral radius",
      "intersecting odd cycles",
      "sharp upper bound",
      "common vertex",
      "extremal graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}