%0 Journal Article
%T On local antimagic chromatic number of various join graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Premalatha, K.
%A Lau, Gee-Choon
%A Arumugam, Subramanian
%A Shiu, W.C.
%D 2023
%\ 12/31/2023
%V 8
%N 4
%P 693-714
%! On local antimagic chromatic number of various join graphs
%K Local antimagic chromatic number
%K join product
%K wheels
%K fans
%R 10.22049/cco.2022.27937.1399
%X 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 $G.$
%U http://comb-opt.azaruniv.ac.ir/article_14428_29f3bfe45780bf0345829025de1c755a.pdf