Face antimagic labelings of plane graphs P_a^b

Suppose G is a finite plane graph with vertex set V(G), edge set E(G) and face set F(G). The paper deals with the problem of labeling the vertices, edges and faces of a plane graph G in such a way that the label of a face and labels of vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph G is called d-antimagic if for every number s, the s-sided face weights form an arithmetic progression of difference d. In this paper we investigate the existence of d-antimagic labelmgs for special class of plane graphs.