{
  "id": "2109.03507",
  "version": "v1",
  "published": "2021-09-08T09:04:52.000Z",
  "updated": "2021-09-08T09:04:52.000Z",
  "title": "Lower bounds for the $\\mathcal{A}_α$-spectral radius of uniform hypergraphs",
  "authors": [
    "Peng-Li Zhang",
    "Xiao-Dong Zhang"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For $0\\leq \\alpha < 1$, the $\\mathcal{A}_{\\alpha}$-spectral radius of a $k$-uniform hypergraph $G$ is defined to be the spectral radius of the tensor $\\mathcal{A}_{\\alpha}(G):=\\alpha \\mathcal{D}(G)+(1-\\alpha) \\mathcal{A}(G)$, where $\\mathcal{D}(G)$ and $A(G)$ are diagonal and the adjacency tensors of $G$ respectively. This paper presents several lower bounds for the difference between the $\\mathcal{A}_{\\alpha}$-spectral radius and an average degree $\\frac{km}{n}$ for a connected $k$-uniform hypergraph with $n$ vertices and $m$ edges, which may be considered as the measures of irregularity of $G$. Moreover, two lower bounds on the $\\mathcal{A}_{\\alpha}$-spectral radius are obtained in terms of the maximum and minimum degrees of a hypergraph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-08T09:04:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C65"
    ],
    "keywords": [
      "spectral radius",
      "uniform hypergraph",
      "lower bounds",
      "average degree",
      "adjacency tensors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}