Group magicness of certain planar graphs

‎Let A be a non-trivial abelian group and A^{*}=A\setminus‎ ‎\{۰\}‎. ‎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