{
  "id": "2408.06703",
  "version": "v1",
  "published": "2024-08-13T07:58:08.000Z",
  "updated": "2024-08-13T07:58:08.000Z",
  "title": "New Families of tripartite graphs with local antimagic chromatic number 3",
  "authors": [
    "Gee-Choon Lau",
    "Wai Chee Shiu"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2408.04942",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a graph $G(V,E)$ of size $q$, a bijection $f : E(G) \\to [1,q]$ is a local antimagc labeling if it induces a vertex labeling $f^+ : V(G) \\to \\mathbb{N}$ such that $f^+(u) \\ne f^+(v)$, where $f^+(u)$ is the sum of all the incident edge label(s) of $u$, for every edge $uv \\in E(G)$. In this paper, we make use of matrices of fixed sizes to construct several families of infinitely many tripartite graphs with local antimagic chromatic number 3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-13T07:58:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78",
      "05C69"
    ],
    "keywords": [
      "local antimagic chromatic number",
      "tripartite graphs",
      "incident edge label",
      "local antimagc labeling"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}