{
  "id": "1110.3497",
  "version": "v2",
  "published": "2011-10-16T16:22:13.000Z",
  "updated": "2013-05-11T21:03:29.000Z",
  "title": "Determinants of Box Products of Paths",
  "authors": [
    "Daniel Pragel"
  ],
  "doi": "10.1016/j.disc.2012.01.038",
  "categories": [
    "math.CO"
  ],
  "abstract": "Suppose that G is the graph obtained by taking the box product of a path of length n and a path of length m. Let M be the adjacency matrix of G. If n=m, H.M. Rara showed in 1996 that det(M)=0. We extend this result to allow n and m to be any positive integers, and show that, if gcd(n+1,m+1)>1, then det(M)=0; otherwise, if gcd(n+1,m+1)=1, then det(M)=(-1)^(nm/2).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-11T21:03:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "box product",
      "determinants",
      "adjacency matrix",
      "positive integers"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.3497P"
    }
  }
}