Suppose is a finite plane graph with vertex set , edge set , and face set . A bijection is called a labeling of type . The weight of a face under a labeling is the sum of the labels (if present) carried by that face and the edges and vertices surrounding it. A labeling of a plane graph is called -\emph{antimagic} if for every number , the set of -sided face weights is
for some integers and (, ), where is the number of -sided faces. We allow different sets for different .
In this paper, we deal with -\emph{antimagic} labelings of type for a special class of plane graphs and we show that a graph has -antimagic labeling for .