{
  "id": "2305.12933",
  "version": "v1",
  "published": "2023-05-22T11:26:17.000Z",
  "updated": "2023-05-22T11:26:17.000Z",
  "title": "On bridge graphs with local antimagic chromatic number 3",
  "authors": [
    "W. C. Shiu",
    "G. C. Lau",
    "R. X. Zhang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G=(V, E)$ be a connected graph. A bijection $f: E\\to \\{1, \\ldots, |E|\\}$ is called a local antimagic labeling if for any two adjacent vertices $x$ and $y$, $f^+(x)\\neq f^+(y)$, where $f^+(x)=\\sum_{e\\in E(x)}f(e)$ and $E(x)$ is the set of edges incident to $x$. Thus a local antimagic labeling induces a proper vertex coloring of $G$, where the vertex $x$ is assigned the color $f^+(x)$. The 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 paper, we present some families of bridge graphs with $\\chi_{la}(G)=3$ and give several ways to construct bridge graphs with $\\chi_{la}(G)=3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-22T11:26:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local antimagic chromatic number",
      "construct bridge graphs",
      "local antimagic labeling induces",
      "adjacent vertices",
      "edges incident"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}