{
  "id": "1008.3646",
  "version": "v2",
  "published": "2010-08-21T17:04:00.000Z",
  "updated": "2012-01-26T20:15:33.000Z",
  "title": "A construction of cospectral graphs for the normalized Laplacian",
  "authors": [
    "Steve Butler",
    "Jason Grout"
  ],
  "comment": "21 pages; lots of figures; includes SAGE code",
  "journal": "S. Butler and J. Grout, A construction of cospectral graphs for the normalized Laplacian, Electronic Journal of Combinatorics 18 (2011), #231, 20pp",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a method to construct cospectral graphs for the normalized Laplacian by a local modification in some graphs with special structure. Namely, under some simple assumptions, we can replace a small bipartite graph with a cospectral mate without changing the spectrum of the entire graph. We also consider a related result for swapping out biregular bipartite graphs for the matrix $A+tD$. We produce (exponentially) large families of non-bipartite, non-regular graphs which are mutually cospectral, and also give an example of a graph which is cospectral with its complement but is not self-complementary.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-26T20:15:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "normalized laplacian",
      "construction",
      "small bipartite graph",
      "construct cospectral graphs",
      "biregular bipartite graphs"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.3646B"
    }
  }
}