{
  "id": "2409.14138",
  "version": "v1",
  "published": "2024-09-21T13:30:34.000Z",
  "updated": "2024-09-21T13:30:34.000Z",
  "title": "A Brualdi-Hoffman-Turán problem for friendship graph",
  "authors": [
    "Fan Chen",
    "Xiying Yuan"
  ],
  "comment": "This article is a draft version and may have some clerical and grammatical errors",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph is said to be $H$-free if it does not contain $H$ as a subgraph. Brualdi-Hoffman-Tur\\'{a}n type problem is to determine the maximum spectral radius of an $H$-free graph $G$ with give size $m$. The $F_k$ is the graph consisting of $k$ triangles that intersect in exactly one common vertex, which is known as the friendship graph. In this paper, we resolve a conjecture (the Brualdi-Hoffman-Tur\\'{a}n-type problem for $F_k$) of Li, Lu and Peng [Discrete Math. 346 (2023) 113680] by using the $k$-core technique presented in Li, Zhai and Shu [European J. Combin, 120 (2024) 103966].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-21T13:30:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "friendship graph",
      "brualdi-hoffman-turán problem",
      "maximum spectral radius",
      "type problem",
      "free graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}