{
  "id": "1910.01374",
  "version": "v1",
  "published": "2019-10-03T09:36:13.000Z",
  "updated": "2019-10-03T09:36:13.000Z",
  "title": "Minimum supports of eigenfunctions with the second largest eigenvalue of the Star graph",
  "authors": [
    "Vladislav Kabanov",
    "Elena V. Konstantinova",
    "Leonid Shalaginov",
    "Alexandr Valyuzhenich"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The Star graph $S_n$, $n\\ge 3$, is the Cayley graph on the symmetric group $Sym_n$ generated by the set of transpositions $\\{(12),(13),\\ldots,(1n)\\}$. In this work we study eigenfunctions of $S_n$ corresponding to the second largest eigenvalue $n-2$. For $n\\ge 8$ and $n=3$, we find the minimum cardinality of the support of an eigenfunction of $S_n$ corresponding to the second largest eigenvalue and obtain a characterization of eigenfunctions with the minimum cardinality of the support.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-03T09:36:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C25",
      "05E15",
      "05B30"
    ],
    "keywords": [
      "second largest eigenvalue",
      "star graph",
      "minimum supports",
      "minimum cardinality",
      "study eigenfunctions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}