{
  "id": "2212.05455",
  "version": "v1",
  "published": "2022-12-11T09:19:01.000Z",
  "updated": "2022-12-11T09:19:01.000Z",
  "title": "Spectral radius and spanning trees of graphs",
  "authors": [
    "Guoyan Ao",
    "Ruifang Liu",
    "Jinjiang Yuan"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For integer $k\\geq2,$ a spanning $k$-ended-tree is a spanning tree with at most $k$ leaves. Motivated by the closure theorem of Broersma and Tuinstra [Independence trees and Hamilton cycles, J. Graph Theory 29 (1998) 227--237], we provide tight spectral conditions to guarantee the existence of a spanning $k$-ended-tree in a connected graph of order $n$ with extremal graphs being characterized. Moreover, by adopting Kaneko's theorem [Spanning trees with constraints on the leaf degree, Discrete Appl. Math. 115 (2001) 73--76], we also present tight spectral conditions for the existence of a spanning tree with leaf degree at most $k$ in a connected graph of order $n$ with extremal graphs being determined, where $k\\geq1$ is an integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-11T09:19:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C35"
    ],
    "keywords": [
      "spanning tree",
      "spectral radius",
      "tight spectral conditions",
      "leaf degree",
      "extremal graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}