{
  "id": "1802.02146",
  "version": "v1",
  "published": "2018-02-06T15:29:51.000Z",
  "updated": "2018-02-06T15:29:51.000Z",
  "title": "On the irregularity of uniform hypergraphs",
  "authors": [
    "Lele Liu",
    "Liying Kang",
    "Erfang Shan"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $H$ be an $r$-uniform hypergraph on $n$ vertices and $m$ edges, and let $d_i$ be the degree of $i\\in V(H)$. Denote by $\\varepsilon(H)$ the difference of the spectral radius of $H$ and the average degree of $H$. Also, denote \\[ s(H)=\\sum_{i\\in V(H)}\\left|d_i-\\frac{rm}{n}\\right|,~ v(H)=\\frac{1}{n}\\sum_{i\\in V(H)}d_i^{\\frac{r}{r-1}}-\\left(\\frac{rm}{n}\\right)^{\\frac{r}{r-1}}. \\] In this paper, we investigate the irregularity of $r$-uniform hypergraph $H$ with respect to $\\varepsilon(H)$, $s(H)$ and $v(H)$, which extend relevant results to uniform hypergraphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-06T15:29:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A42",
      "05C50"
    ],
    "keywords": [
      "uniform hypergraph",
      "irregularity",
      "extend relevant results",
      "average degree",
      "spectral radius"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}