{
  "id": "2209.03120",
  "version": "v1",
  "published": "2022-09-07T13:10:19.000Z",
  "updated": "2022-09-07T13:10:19.000Z",
  "title": "The signless Laplacian spectral radius of graphs without trees",
  "authors": [
    "Ming-Zhu Chen",
    "Zhao-Ming Li",
    "Xiao-Dong Zhang"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $Q(G)=D(G)+A(G)$ be the signless Laplacian matrix of a simple graph of order $n$, where $D(G)$ and $A(G)$ are the degree diagonal matrix and the adjacency matrix of $G$, respectively. In this paper, we present a sharp upper bound for the signless spectral radius of $G$ without any tree and characterize all extremal graphs which attain the upper bound, which may be regarded as a spectral extremal version for the famous Erd\\H{o}s-S\\'{o}s conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-07T13:10:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C35"
    ],
    "keywords": [
      "signless laplacian spectral radius",
      "degree diagonal matrix",
      "spectral extremal version",
      "sharp upper bound",
      "extremal graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}