@article {
author = {Premalatha, K. and Lau, Gee-Choon and Arumugam, Subramanian and Shiu, W.C.},
title = {On local antimagic chromatic number of various join graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {8},
number = {4},
pages = {693-714},
year = {2023},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2022.27937.1399},
abstract = {A local antimagic edge labeling of a graph $G=(V,E)$ is a bijection $f:E\rightarrow\{1,2,\dots,|E|\}$ such that the induced vertex labeling $f^+:V\rightarrow \mathbb{Z}$ given by $f^+(u)=\sum f(e),$ where the summation runs over all edges $e$ incident to $u,$ has the property that any two adjacent vertices have distinct labels. A graph $G$ is said to be locally antimagic if it admits a local antimagic edge labeling. The local antimagic chromatic number $\chi_{la}(G)$ is the minimum number of distinct induced vertex labels over all local antimagic labelings of $G.$ In this paper we obtain sufficient conditions under which $\chi_{la}(G\vee H),$ where $H$ is either a cycle or the empty graph $O_n=\overline{K_n},$ satisfies a sharp upper bound. Using this we determine the value of $\chi_{la}(G\vee H)$ for many wheel related graphs $G.$},
keywords = {Local antimagic chromatic number,join product,wheels,fans},
url = {http://comb-opt.azaruniv.ac.ir/article_14428.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14428_29f3bfe45780bf0345829025de1c755a.pdf}
}