{
  "id": "2301.03389",
  "version": "v1",
  "published": "2022-11-02T03:05:40.000Z",
  "updated": "2022-11-02T03:05:40.000Z",
  "title": "On the $α$-index of minimally 2-connected graphs with given order or size",
  "authors": [
    "Jiayu Lou",
    "Ligong Wang",
    "Ming Yuan"
  ],
  "comment": "15 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "For any real $\\alpha \\in [0,1]$, Nikiforov defined the $A_\\alpha$-matrix of a graph $G$ as $A_\\alpha(G)=\\alpha D(G)+(1-\\alpha)A(G)$, where $A(G)$ and $D(G)$ are the adjacency matrix and the diagonal matrix of vertex degrees of $G$, respectively. The largest eigenvalue of $A_\\alpha(G)$ is called the $\\alpha$-index or the $A_\\alpha$-spectral radius of $G$. A graph is minimally $k$-connected if it is $k$-connected and deleting any arbitrary chosen edge always leaves a graph which is not $k$-connected. In this paper, we characterize the extremal graphs with the maximum $\\alpha$-index for $\\alpha \\in [\\frac{1}{2},1)$ among all minimally 2-connected graphs with given order or size, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-02T03:05:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C40",
      "05C35"
    ],
    "keywords": [
      "arbitrary chosen edge",
      "extremal graphs",
      "adjacency matrix",
      "diagonal matrix",
      "spectral radius"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}