{
  "id": "2212.14525",
  "version": "v1",
  "published": "2022-12-30T02:59:31.000Z",
  "updated": "2022-12-30T02:59:31.000Z",
  "title": "Maxima of the $Q$-index of non-bipartite graphs: forbidden short odd cycles",
  "authors": [
    "Lu Miao",
    "Ruifang Liu",
    "Jie Xue"
  ],
  "comment": "15 pages, 5 figures. arXiv admin note: text overlap with arXiv:2209.00801",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a non-bipartite graph which does not contain any odd cycle of length at most $2k+1$. In this paper, we determine the maximum $Q$-index of $G$ if its order is fixed, and the corresponding extremal graph is uniquely characterized. Moreover, if the size of $G$ is given, the maximum $Q$-index of $G$ and the unique extremal graph are also proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-30T02:59:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C35"
    ],
    "keywords": [
      "forbidden short odd cycles",
      "non-bipartite graph",
      "unique extremal graph",
      "corresponding extremal graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}