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.
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Nikmehr, M. J., & Bahramian, S. (2014). Group magicness of certain planar graphs. Transactions on Combinatorics, 3(2), 1-9. doi: 10.22108/toc.2014.4268
MLA
Mohammad Javad Nikmehr; Samaneh Bahramian. "Group magicness of certain planar graphs". Transactions on Combinatorics, 3, 2, 2014, 1-9. doi: 10.22108/toc.2014.4268
HARVARD
Nikmehr, M. J., Bahramian, S. (2014). 'Group magicness of certain planar graphs', Transactions on Combinatorics, 3(2), pp. 1-9. doi: 10.22108/toc.2014.4268
VANCOUVER
Nikmehr, M. J., Bahramian, S. Group magicness of certain planar graphs. Transactions on Combinatorics, 2014; 3(2): 1-9. doi: 10.22108/toc.2014.4268
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