{
  "id": "2408.04942",
  "version": "v1",
  "published": "2024-08-09T08:48:29.000Z",
  "updated": "2024-08-09T08:48:29.000Z",
  "title": "On local antimagic chromatic numbers of the join of two special families of graphs",
  "authors": [
    "Gee-Choon Lau",
    "Wai Chee Shiu"
  ],
  "comment": "15 pages, 8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "It is known that null graphs and 1-regular graphs are the only regular graphs without local antimagic chromatic number. In this paper, we use matrices of size $(2m+1) \\times (2k+1)$ to completely determine the local antimagic chromatic number of the join of null graphs, $O_m, m\\ge 1,$ and 1-regular graphs of odd components, $(2k+1)P_2$, $k\\ge 1$. Consequently, we obtained infinitely many (possibly disconnected or regular) tripartite graphs with local antimagic chromatic number 3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-09T08:48:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78",
      "05C69"
    ],
    "keywords": [
      "local antimagic chromatic number",
      "special families",
      "null graphs",
      "regular graphs",
      "tripartite graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}