{
  "id": "1601.07647",
  "version": "v1",
  "published": "2016-01-28T05:08:59.000Z",
  "updated": "2016-01-28T05:08:59.000Z",
  "title": "Perfect State Transfer on Cayley graphs over finite abelian groups",
  "authors": [
    "Hiranmoy Pal",
    "Bikash Bhattacharjya"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study perfect state transfer (with respect to adjacency matrix) on Cayley graph over finite abelian groups. We find that if a Cayley graph over a finite abelian group exhibits perfect state transfer then it must have integral spectrum. A gcd-graph is a Cayley graph over a finite abelian group defined by greatest common divisors. It is well known that all gcd-graphs have integral spectrum. We find a sufficient condition for a gcd-graph to have periodicity and perfect state transfer at $\\frac{\\pi}{2}$. Also we find a necessary and sufficient condition for a particular class of gcd-graphs to be periodic at $\\pi$. Using that we find that there are some gcd-graphs not exhibiting perfect state transfer at $\\frac{\\pi}{2^{k}}$ for all positive integers $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-28T05:08:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite abelian group",
      "cayley graph",
      "sufficient condition",
      "integral spectrum",
      "study perfect state transfer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160107647P"
    }
  }
}