{
  "id": "1901.08629",
  "version": "v1",
  "published": "2019-01-24T20:08:39.000Z",
  "updated": "2019-01-24T20:08:39.000Z",
  "title": "Realization of digraphs in Abelian groups and its consequences",
  "authors": [
    "Sylwia Cichacz",
    "Zsolt Tuza"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\overrightarrow{G}$ be a directed graph with no component of orderless than~$3$, and let $\\Gamma$ be a finite Abelian group such that $|\\Gamma|\\geq 4|V(\\overrightarrow{G})|$ or if $|V(\\overrightarrow{G})|$ is large enough with respect to an arbitrarily fixed $\\varepsilon>0$ then $|\\Gamma|\\geq (1+\\varepsilon)|V(\\overrightarrow{G})|$. We show that there exists an injective mapping $\\varphi$ from $V(\\overrightarrow{G})$ to the group $\\Gamma$ such that $\\sum_{x\\in V(C)}\\varphi(x) = 0$ for every connected component $C$ of $\\overrightarrow{G}$, where $0$ is the identity element of $\\Gamma$. Moreover we show some applications of this result to group distance magic labelings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-24T20:08:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "realization",
      "consequences",
      "group distance magic labelings",
      "finite abelian group",
      "identity element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}