{
  "id": "2010.04624",
  "version": "v1",
  "published": "2020-10-09T15:08:33.000Z",
  "updated": "2020-10-09T15:08:33.000Z",
  "title": "Maximum spectral radius of outerplanar 3-uniform hypergraphs",
  "authors": [
    "M. N. Ellingham",
    "Linyuan Lu",
    "Zhiyu Wang"
  ],
  "comment": "13 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we study the maximum spectral radius of outerplanar $3$-uniform hypergraphs. Given a hypergraph $\\mathcal{H}$, the shadow of $\\mathcal{H}$ is a graph $G$ with $V(G)= V(\\mathcal{H})$ and $E(G) = \\{uv: uv \\in h \\textrm{ for some } h\\in E(\\mathcal{H})\\}$. A graph is outerplanar if it can be embedded in the plane such that all its vertices lie on the outer face. A $3$-uniform hypergraph $\\mathcal{H}$ is called outerplanar if its shadow has an outerplanar embedding such that every hyperedge of $\\mathcal{H}$ is the vertex set of an interior triangular face of the shadow. Cvetkovi\\'c and Rowlinson [Linear and Multilinear Algebra, 1990] conjectured that among all outerplanar graphs on $n$ vertices, the graph $K_1+ P_{n-1}$ attains the maximum spectral radius. We show a hypergraph analogue of the Cvetkovi\\'c-Rowlinson conjecture. In particular, we show that for sufficiently large $n$, the $n$-vertex outerplanar $3$-uniform hypergraph of maximum spectral radius is the unique $3$-uniform hypergraph whose shadow is $K_1 + P_{n-1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-09T15:08:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C65",
      "05C50"
    ],
    "keywords": [
      "maximum spectral radius",
      "uniform hypergraph",
      "interior triangular face",
      "outer face",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}