{
  "id": "1604.04275",
  "version": "v1",
  "published": "2016-04-14T19:43:34.000Z",
  "updated": "2016-04-14T19:43:34.000Z",
  "title": "Remarks on the energy of regular graphs",
  "authors": [
    "V. Nikiforov"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "This note is about the energy of regular graphs. The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. It is shown that graphs that are close to regular can be made regular with a negligible change of the energy. Also a $k$-regular graph can be extended to a $k$-regular graph of a slightly larger order with almost the same energy. As an application, it is shown that for every sufficiently large $n,$ there exists a regular graph $G$ of order $n$ whose energy $\\left\\Vert G\\right\\Vert _{\\ast}$ satisfies \\[ \\left\\Vert G\\right\\Vert _{\\ast}>\\frac{1}{2}n^{3/2}-n^{13/10}. \\] Several infinite families of graphs with maximal or submaximal energy are given, and the energy of almost all regular graphs is determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-14T19:43:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "regular graph",
      "slightly larger order",
      "submaximal energy",
      "absolute values",
      "infinite families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404275N"
    }
  }
}