{
  "id": "1808.04956",
  "version": "v1",
  "published": "2018-08-15T03:23:53.000Z",
  "updated": "2018-08-15T03:23:53.000Z",
  "title": "On Local Antimagic Vertex Coloring for Corona Products of Graphs",
  "authors": [
    "S. Arumugam",
    "Yi-Chun Lee",
    "K. Premalatha",
    "Tao-Ming Wang"
  ],
  "comment": "29 pages, 16 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G = (V, E)$ be a finite simple undirected graph without $K_2$ components. A bijection $f : E \\rightarrow \\{1, 2,\\cdots, |E|\\}$ is called a {\\bf local antimagic labeling} if for any two adjacent vertices $u$ and $v$, they have different vertex sums, i.e. $w(u) \\neq w(v)$, where the vertex sum $w(u) = \\sum_{e \\in E(u)} f(e)$, and $E(u)$ is the set of edges incident to $u$. Thus any local antimagic labeling induces a proper vertex coloring of $G$ where the vertex $v$ is assigned the color(vertex sum) $w(v)$. The {\\bf local antimagic chromatic number} $\\chi_{la}(G)$ is the minimum number of colors taken over all colorings induced by local antimagic labelings of $G$. In this article among others we determine completely the local antimagic chromatic number $\\chi_{la}(G\\circ \\overline{K_m})$ for the corona product of a graph $G$ with the null graph $\\overline{K_m}$ on $m\\geq 1$ vertices, when $G$ is a path $P_n$, a cycle $C_n$, and a complete graph $K_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-15T03:23:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C78"
    ],
    "keywords": [
      "local antimagic vertex coloring",
      "corona product",
      "local antimagic chromatic number",
      "vertex sum",
      "local antimagic labeling induces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}