{
  "id": "2002.03584",
  "version": "v1",
  "published": "2020-02-10T07:48:34.000Z",
  "updated": "2020-02-10T07:48:34.000Z",
  "title": "Optimal embedding and spectral gap of a finite graph",
  "authors": [
    "Takumi Gomyou",
    "Toshimasa Kobayashi",
    "Takefumi Kondo",
    "Shin Nayatani"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a new optimization problem regarding embeddings of a graph into a Euclidean space and discuss its relation to the two, mutually dual, optimizations problems introduced by Goering-Helmberg-Wappler. We prove that the Laplace eigenvalue maximization problem of Goering et al is also dual to our embedding optimization problem. We solve the optimization problems for generalized polygons and graphs isomorphic to the one-skeltons of regular and semi-regular polyhedra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-10T07:48:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C62",
      "05C50"
    ],
    "keywords": [
      "spectral gap",
      "finite graph",
      "optimal embedding",
      "laplace eigenvalue maximization problem",
      "optimization problem regarding embeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}