## Abstract

Let G = (V, E) be a graph with order n =|V| and size m =|E|. A bijection f: E → {1,2, . . ., m} is called a local antimagic labeling if for any adjacent vertices u and v, w(u) ≠ w(v) with w(u) = ?_{uv?E(u)} f(uv), where E(u) is the set of edges incident to u. A graph G is called local antimagic graph if it has local antimagic labeling. The local antimagic chromatic number of G is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. The corona product of two graphs G and H is the graph G ∘ H obtained by taking one copy of G and n copies of H and joining the i^{th} vertex of G to every vertex in the i^{th} copy of H. In this study, we determine the local antimagic chromatic number for (P_{?} K_{1}) ∘ K_{1} where Pₙ is a path of order n for n is even and n ≥ 4.

Original language | English |
---|---|

Article number | 020007 |

Journal | AIP Conference Proceedings |

Volume | 3176 |

Issue number | 1 |

DOIs | |

Publication status | Published - 30 Jul 2024 |

Event | 7th International Conference of Combinatorics, Graph Theory, and Network Topology, ICCGANT 2023 - Hybrid, Jember, Indonesia Duration: 21 Nov 2023 → 22 Nov 2023 |

## Fingerprint

Dive into the research topics of 'Local Antimagic Labeling of (P_{?}° K

_{1}) ° K

_{1}'. Together they form a unique fingerprint.