A note on local edge antimagic chromatic number of graphs

Hadiputra, Fawwaz Fakhrurrozi ^[1] ; Maryati, Tita Khalis ^[2]
1. [1] Institut Teknologi Bandung (ITB)
2. [2] UIN Syarif Hidayatullah Jakarta
Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 43, Nº. 2, 2024, págs. 447-458
Idioma: inglés
DOI: 10.22199/issn.0717-6279-6014
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Resumen
- Let $G$ be a finite, undirected and simple graph. A bijection $f : V(G) \to [1,|V(G)|]$ is called a local edge antimagic labeling if for any two adjacent edges $uv,vw \in E(G), f(u) \ne f(w)$. The local edge antimagic chromatic number $\ch(G)$ is the minimum number of colors taken over all colorings induced by local edge antimagic labeling of $G$. In this paper, we investigate characterization of graphs $G$ with small number $\ch(G)$, relationship between local edge antimagic chromatic number $\ch(G)$ and edge independence number $\alpha'(G)$, and bounds of $\ch(G)$ for any graphs.