{
  "id": "2007.08627",
  "version": "v1",
  "published": "2020-07-15T12:17:06.000Z",
  "updated": "2020-07-15T12:17:06.000Z",
  "title": "The signless Laplacian spectral radius of graphs with forbidding linear forests",
  "authors": [
    "Ming-Zhu Chen",
    "A-Ming Liu",
    "Xiao-Dong Zhang"
  ],
  "comment": "14 pagew, 2 figures. arXiv admin note: text overlap with arXiv:1801.06763",
  "journal": "Linear algebra Application 591(2020)25-43",
  "categories": [
    "math.CO"
  ],
  "abstract": "Tur\\'{a}n type extremal problem is how to maximize the number of edges over all graphs which do not contain fixed forbidden subgraphs. Similarly, spectral Tur\\'{a}n type extremal problem is how to maximize (signless Laplacian) spectral radius over all graphs which do not contain fixed subgraphs. In this paper, we first present a stability result for $k\\cdot P_3$ in terms of the number of edges and then determine all extremal graphs maximizing the signless Laplacian spectral radius over all graphs which do not contain a fixed linear forest with at most two odd paths or $k\\cdot P_3$ as a subgraph, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-15T12:17:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "signless laplacian spectral radius",
      "forbidding linear forests",
      "type extremal problem",
      "contain fixed forbidden subgraphs"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}