{
  "id": "1807.08112",
  "version": "v1",
  "published": "2018-07-21T09:33:32.000Z",
  "updated": "2018-07-21T09:33:32.000Z",
  "title": "On the $α$-spectral radius of uniform hypergraphs",
  "authors": [
    "HaiYan Guo",
    "Bo Zhou"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For $0\\le\\alpha<1$ and a uniform hypergraph $G$, the $\\alpha$-spectral radius of $G$ is the largest $H$-eigenvalue of $\\alpha \\mathcal{D}(G) +(1-\\alpha)\\mathcal{A}(G)$, where $\\mathcal{D}(G)$ and $\\mathcal{A}(G)$ are the diagonal tensor of degrees and the adjacency tensor of $G$, respectively. We give upper bounds for the $\\alpha$-spectral radius of a uniform hypergraph, propose some transformations that increase the $\\alpha$-spectral radius, and determine the unique hypergraphs with maximum $\\alpha$-spectral radius in some classes of uniform hypergraphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-21T09:33:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral radius",
      "uniform hypergraph",
      "unique hypergraphs",
      "adjacency tensor",
      "upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}