group magicness of certain planar graphs

let $a$ be a non-trivial abelian group and $a^{*}=asetminus {0}$. 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 $$l^+(v)=sum_{uvin e(g)} l(uv)$$ is a constant map.the set of all constant integerssuch that $sum_{uin n(v)} l(uv)=c$, for each $vin n(v)$,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 thispaper we determine the index set of certain planar graphsfor $mathbb{z}_{h}$, where $hin mathbb{n}$, such as wheels and fans.