Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231231On local antimagic chromatic number of various join graphs6937141442810.22049/cco.2022.27937.1399ENK.PremalathaKalasalingam Academy of Research and EducationGee-ChoonLauUniversiti Teknologi MARA,
Faculty of Computer
and Mathematical Sciences,
85100 Segamat,
Johor, Malaysia0000-0002-9777-6571SubramanianArumugamDirector (n-CARDMATH)
Kalasalingam University
Anand Nagar, Krishnankoil-626 126
Tamil Nadu, India0000-0002-4477-9453W.C.ShiuDepartment of Mathematics,
The Chinese University of Hong Kong,
Shatin, Hong Kong, P.R. China.Journal Article20220626A 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 $G.$http://comb-opt.azaruniv.ac.ir/article_14428_29f3bfe45780bf0345829025de1c755a.pdf