Local distance antimagic cromatic number of join product of graphs with cycles or paths

Authors : Waichee Shiu, Geechoon Lau, Nalliah M

Pages : 788-802

Doi:10.15672/hujms.1266085

View : 95 | Download : 221

Publication Date : 2024-06-27

Article Type : Research Paper

Abstract :Let $G$ be a graph of order $p$ without isolated vertices. A bijection $f: V \\to \\{1,2,3,\\dots,p\\}$ is called a local distance antimagic labeling, if $w_f(u)\\ne w_f(v)$ for every edge $uv$ of $G$, where $w_f(u)=\\sum_{x\\epsilon N(u)} {f(x)}$. The local distance antimagic chromatic number $\\chi_{lda}(G)$ is defined to be the minimum number of colors taken over all colorings of $G$ induced by local distance antimagic labelings of $G$. In this paper, we determined the local distance antimagic chromatic number of some cycles, paths, disjoint union of 3-paths. We also determined the local distance antimagic chromatic number of join products of some graphs with cycles or paths.
Keywords : local distance antimagic chromatic number, join product, cycle, path, null graph