{
  "id": "1801.00438",
  "version": "v1",
  "published": "2018-01-01T12:34:24.000Z",
  "updated": "2018-01-01T12:34:24.000Z",
  "title": "On eigenfunctions and maximal cliques of Paley graphs of square order",
  "authors": [
    "Sergey Goryainov",
    "Vladislav V. Kabanov",
    "Leonid Shalaginov",
    "Alexandr Valyuzhenich"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we find new maximal cliques of size $\\frac{q+1}{2}$ or $\\frac{q+3}{2}$, accordingly as $q\\equiv 1(4)$ or $q\\equiv 3(4)$, in Paley graphs of order $q^2$, where $q$ is an odd prime power. After that we use new cliques to define a family of eigenfunctions corresponding to both non-principal eigenvalues and having the cardinality of support $q+1$, which is the minimum by the weight-distribution bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-01T12:34:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximal cliques",
      "paley graphs",
      "square order",
      "eigenfunctions",
      "odd prime power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}