@article {
author = {Nikmehr, Mohammad Javad and Bahramian, Samaneh},
title = {Group magicness of certain planar graphs},
journal = {Transactions on Combinatorics},
volume = {3},
number = {2},
pages = {1-9},
year = {2014},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2014.4268},
abstract = {Let $A$ be a non-trivial abelian group and $A^{*}=A\setminus \{0\}$. A graph $G$ is said to be $A$-magic graph if there exists a labeling $l:E(G)\rightarrow A^{*}$ such that the induced vertex labeling $l^{+}:V(G)\rightarrow A$, define by $$l^+(v)=\sum_{uv\in E(G)} l(uv)$$ is a constant map. The set of all constant integers such that $\sum_{u\in N(v)} l(uv)=c$, for each $v\in N(v)$, where $N(v)$ denotes the set of adjacent vertices to vertex $v$ in $G$, is called the index set of $G$ and denoted by ${\rm In}_{A}(G).$ In this paper we determine the index set of certain planar graphs for $\mathbb{Z}_{h}$, where $h\in \mathbb{N}$, such as wheels and fans.},
keywords = {Index Set,Magic,Zero-Sum,Null Set},
url = {https://toc.ui.ac.ir/article_4268.html},
eprint = {https://toc.ui.ac.ir/article_4268_04ba14cdbc2db53b8eb1ac8d76755788.pdf}
}