{
  "id": "1805.04888",
  "version": "v1",
  "published": "2018-05-13T13:51:40.000Z",
  "updated": "2018-05-13T13:51:40.000Z",
  "title": "On local antimagic chromatic number of cycle-related join graphs",
  "authors": [
    "Gee-Choon Lau",
    "Wai-Chee Shiu",
    "Ho-Kuen Ng"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f:E \\to\\{1,\\ldots ,|E|\\}$ such that for any pair of adjacent vertices $x$ and $y$, $f^+(x)\\not= f^+(y)$, where the induced vertex label $f^+(x)= \\sum f(e)$, with $e$ ranging over all the edges incident to $x$. The local antimagic chromatic number of $G$, denoted by $\\chi_{la}(G)$, is the minimum number of distinct induced vertex labels over all local antimagic labelings of $G$. In this paper, several sufficient conditions for $\\chi_{la}(H)\\le \\chi_{la}(G)$ are obtained, where $H$ is obtained from $G$ with a certain edge deleted or added. We then determined the exact value of the local antimagic chromatic number of many cycle related join graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-13T13:51:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78",
      "05C69"
    ],
    "keywords": [
      "local antimagic chromatic number",
      "cycle-related join graphs",
      "distinct induced vertex labels",
      "cycle related join graphs",
      "local antimagic labelings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}