{
  "id": "2412.02179",
  "version": "v1",
  "published": "2024-12-03T05:26:16.000Z",
  "updated": "2024-12-03T05:26:16.000Z",
  "title": "Maximization of the first Laplace eigenvalue of a finite graph II",
  "authors": [
    "Takumi Gomyou",
    "Shin Nayatani"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a length function on the set of edges of a finite graph, the corresponding Fujiwara Laplacian is defined. We consider a problem of maximizing the first nonzero eigenvalue of this graph Laplacian over all choices of edge-length function subject to a certain normalization. In this paper we prove that the supremum of the first nonzero eigenvalue is infinite whenever the graph contains a cycle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-03T05:26:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C62",
      "05C50"
    ],
    "keywords": [
      "first laplace eigenvalue",
      "finite graph",
      "first nonzero eigenvalue",
      "maximization",
      "edge-length function subject"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}