{
  "id": "1601.07398",
  "version": "v1",
  "published": "2016-01-27T14:58:59.000Z",
  "updated": "2016-01-27T14:58:59.000Z",
  "title": "A class of gcd-graphs having Perfect State Transfer",
  "authors": [
    "Hiranmoy Pal",
    "Bikash Bhattacharjya"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph with adjacency matrix $A$. The transition matrix corresponding to $G$ is defined by $H(t):=\\exp{\\left(itA\\right)}$, $t\\in\\Rl$. The graph $G$ is said to have perfect state transfer (PST) from a vertex $u$ to another vertex $v$, if there exist $\\tau\\in\\Rl$ such that the $uv$-th entry of $H(\\tau)$ has unit modulus. The graph $G$ is said to be periodic at $\\tau\\in\\Rl$ if there exist $\\gamma\\in\\Cl$ with $|\\gamma|=1$ such that $H(\\tau)=\\gamma I$, where $I$ is the identity matrix. A $\\mathit{gcd}$-graph is a Cayley graph over a finite abelian group defined by greatest common divisors. In this paper, we construct classes of $\\mathit{gcd}$-graphs having periodicity and perfect state transfer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-27T14:58:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perfect state transfer",
      "gcd-graphs",
      "finite abelian group",
      "greatest common divisors",
      "adjacency matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160107398P"
    }
  }
}