{
  "id": "2303.16687",
  "version": "v1",
  "published": "2023-03-29T13:38:14.000Z",
  "updated": "2023-03-29T13:38:14.000Z",
  "title": "Signless Laplacian spectral radius for a k-extendable graph",
  "authors": [
    "Sizhong Zhou",
    "Yuli Zhang"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $k$ and $n$ be two nonnegative integers with $n\\equiv0$ (mod 2), and let $G$ be a graph of order $n$ with a 1-factor. Then $G$ is said to be $k$-extendable for $0\\leq k\\leq\\frac{n-2}{2}$ if every matching in $G$ of size $k$ can be extended to a 1-factor. In this paper, we first establish a lower bound on the signless Laplacian spectral radius of $G$ to ensure that $G$ is $k$-extendable. Then we create some extremal graphs to claim that all the bounds derived in this article are sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-29T13:38:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C70"
    ],
    "keywords": [
      "signless laplacian spectral radius",
      "k-extendable graph",
      "lower bound",
      "extremal graphs",
      "nonnegative integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}