{
  "id": "0808.2234",
  "version": "v2",
  "published": "2008-08-16T03:27:11.000Z",
  "updated": "2009-05-13T23:10:28.000Z",
  "title": "Sum of squares of degrees in a graph",
  "authors": [
    "Bernardo M. Ábrego",
    "Silvia Fernández-Merchant",
    "Michael G. Neubauer",
    "William Watkins"
  ],
  "comment": "40 pages, 11 figures. Updated introduction, a minor issue on the definition of Quasi-complete graphs was fixed, and a couple of references were added",
  "journal": "J. Inequal. Pure Appl. Math. 10 (2009), no. 3, Article 64, 34 pp",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\G(v,e)$ be the set of all simple graphs with $v$ vertices and $e$ edges and let $P_2(G)=\\sum d_i^2$ denote the sum of the squares of the degrees, $d_1, >..., d_v$, of the vertices of $G$. It is known that the maximum value of $P_2(G)$ for $G \\in \\G(v,e)$ occurs at one or both of two special graphs in $\\G(v,e)$--the \\qs graph or the \\qc graph. For each pair $(v,e)$, we determine which of these two graphs has the larger value of $P_2(G)$. We also determine all pairs $(v,e)$ for which the values of $P_2(G)$ are the same for the \\qs and the \\qc graph. In addition to the \\qs and \\qc graphs, we find all other graphs in $\\G(v,e)$ for which the maximum value of $P_2(G)$ is attained. Density questions posed by previous authors are examined.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-13T23:10:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C07",
      "05C35"
    ],
    "keywords": [
      "maximum value",
      "simple graphs",
      "special graphs",
      "larger value",
      "density questions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.2234A"
    }
  }
}