{
  "id": "1705.09790",
  "version": "v1",
  "published": "2017-05-27T09:04:03.000Z",
  "updated": "2017-05-27T09:04:03.000Z",
  "title": "Maximum nullity of Cayley graph",
  "authors": [
    "Ebrahim Vatandoost",
    "Yasser Golkhandy Pour"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "One of the most interesting problems on maximum nullity (minimum rank) is to characterize $M(\\mathcal{G})$ ($mr(\\mathcal{G})$) for a graph $\\mathcal{G}$. In this regard, many researchers have been trying to find an upper or lower bound for the maximum nullity. For more results on this topic, see \\cite{4}, \\cite{2}, \\cite{10} and \\cite{1}. In this paper, by using a result of Babai \\cite{Babai}, which presents the spectrum of a Cayley graph in terms of irreducible characters of the underlying group, and using representation and character of groups, we give a lower bound for the maximum nullity of Cayley graph, $X_S(G)$, where $G=\\langle a\\rangle$ is a cyclic group, or $G=G_1\\times \\cdots\\times G_t$ such that $G_1=\\langle a\\rangle$ is a cyclic group and $G_i$ is an arbitrary finite group, for some $2\\leq i\\leq t$, with determine the spectrum of Cayley graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-27T09:04:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "maximum nullity",
      "cayley graph",
      "lower bound",
      "cyclic group",
      "arbitrary finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}