{
  "id": "1407.5193",
  "version": "v1",
  "published": "2014-07-19T14:59:01.000Z",
  "updated": "2014-07-19T14:59:01.000Z",
  "title": "Some spectral properties of uniform hypergraphs",
  "authors": [
    "Jiang Zhou",
    "Lizhu Sun",
    "Wenzhe Wang",
    "Changjiang Bu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For a $k$-uniform hypergraph $H$, we obtain some trace formulas for the Laplacian tensor of $H$, which imply that $\\sum_{i=1}^nd_i^s$ ($s=1,\\ldots,k$) is determined by the Laplacian spectrum of $H$, where $d_1,\\ldots,d_n$ is the degree sequence of $H$. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spectral characterizations of odd-bipartite hypergraphs, and give a partial answer to a question posed by Shao et al \\cite{ShaoShanWu}. We also give some spectral properties of power hypergraphs, and show that a conjecture posed by Hu et al \\cite{HuQiShao} holds under certain conditons.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-19T14:59:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniform hypergraph",
      "spectral properties",
      "trace formulas",
      "laplacian tensor",
      "laplacian polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.5193Z"
    }
  }
}