{
  "id": "1606.06782",
  "version": "v1",
  "published": "2016-06-21T21:43:12.000Z",
  "updated": "2016-06-21T21:43:12.000Z",
  "title": "A construction of distance cospectral graphs",
  "authors": [
    "Kristin Heysse"
  ],
  "comment": "17 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The distance matrix of a connected graph is the symmetric matrix with columns and rows indexed by the vertices and entries that are the pairwise distances between the corresponding vertices. We give a construction for graphs which differ in their edge counts yet are cospectral with respect to the distance matrix. Further, we identify a subgraph switching behavior which constructs additional distance cospectral graphs. The proofs for both constructions rely on a perturbation of (most of) the distance eigenvectors of one graph to yield the distance eigenvectors of the other.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-21T21:43:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "construction",
      "constructs additional distance cospectral graphs",
      "distance matrix",
      "distance eigenvectors",
      "edge counts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}