{
  "id": "2308.07278",
  "version": "v1",
  "published": "2023-08-14T17:10:11.000Z",
  "updated": "2023-08-14T17:10:11.000Z",
  "title": "Local antimagic chromatic number of partite graphs",
  "authors": [
    "C. R. Pavithra",
    "A. V. Prajeesh",
    "V. S. Sarath"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a connected graph with $|V| = n$ and $|E| = m$. A bijection $f:E\\rightarrow \\{1,2,...,m\\}$ is called a local antimagic labeling of $G$ if for any two adjacent vertices $u$ and $v$, $w(u) \\neq w(v)$, where $w(u) = \\sum_{e \\in E(u)}f(e)$, 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 $w(v)$. The local antimagic chromatic number is the minimum number of colors taken over all colorings induced by local antimagic labelings of $G$. Let $m,n > 1$. In this paper, the local antimagic chromatic number of a complete tripartite graph $K_{1,m,n}$, and $r$ copies of a complete bipartite graph $K_{m,n}$ where $m \\not \\equiv n \\bmod 2$ are determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-14T17:10:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78"
    ],
    "keywords": [
      "local antimagic chromatic number",
      "partite graphs",
      "complete bipartite graph",
      "local antimagic labeling induces",
      "complete tripartite graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}