TY - JOUR
ID - 14428
TI - On local antimagic chromatic number of various join graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Premalatha, K.
AU - Lau, Gee-Choon
AU - Arumugam, Subramanian
AU - Shiu, W.C.
AD - Kalasalingam Academy of Research and Education
AD - Universiti Teknologi MARA,
Faculty of Computer
and Mathematical Sciences,
85100 Segamat,
Johor, Malaysia
AD - Director (n-CARDMATH)
Kalasalingam University
Anand Nagar, Krishnankoil-626 126
Tamil Nadu, India
AD - Department of Mathematics,
The Chinese University of Hong Kong,
Shatin, Hong Kong, P.R. China.
Y1 - 2023
PY - 2023
VL - 8
IS - 4
SP - 693
EP - 714
KW - Local antimagic chromatic number
KW - join product
KW - wheels
KW - fans
DO - 10.22049/cco.2022.27937.1399
N2 - 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 $G.$
UR - http://comb-opt.azaruniv.ac.ir/article_14428.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14428_29f3bfe45780bf0345829025de1c755a.pdf
ER -