@article {
author = {Shaebani, S.},
title = {ON LOCAL ANTIMAGIC CHROMATIC NUMBER OF GRAPHS},
journal = {Journal of Algebraic Systems},
volume = {7},
number = {2},
pages = {245-256},
year = {2020},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2019.7933.1391},
abstract = {A {\it local antimagic labeling} of a connected graph $G$ with at least three vertices, is a bijection $f:E(G) \rightarrow \{1,2,\ldots , |E(G)|\}$ such that for any two adjacent vertices $u$ and $v$ of $G$, the condition $\omega _{f}(u) \neq \omega _{f}(v)$ holds; where $\omega _{f}(u)=\sum _{x\in N(u)} f(xu)$. Assigning $\omega _{f}(u)$ to $u$ for each vertex $u$ in $V(G)$, induces naturally a proper vertex coloring of $G$; and $|f|$ denotes the number of colors appearing in this proper vertex coloring. The {\it local antimagic chromatic number} of $G$, denoted by $\chi _{la}(G)$, is defined as the minimum of $|f|$, where $f$ ranges over all local antimagic labelings of $G$. In this paper, we explicitly construct an infinite class of connected graphs $G$ such that $\chi _{la}(G)$ can be arbitrarily large while $\chi _{la}(G \vee \bar{K_{2}})=3$, where $G \vee \bar{K_{2}}$ is the join graph of $G$ and the complement graph of $K_{2}$. The aforementioned fact leads us to an infinite class of counterexamples to a result of [Local antimagic vertex coloring of a graph, Graphs and Combinatorics 33} (2017), 275-285].},
keywords = {Antimagic labeling,Local antimagic labeling,Local antimagic chromatic number},
url = {http://jas.shahroodut.ac.ir/article_1593.html},
eprint = {http://jas.shahroodut.ac.ir/article_1593_af1188905d11cbb4a0f2430b514d9ffb.pdf}
}