Face antimagic labelings of antiprisms

Abstract

The paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called dantimagic if for every positive integer s, the s-sided face weights form an arithmetic progression with a difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper we will consider the antiprism as three cycle parts. The super d-antimagic labelings, for d = 0,1,..., 6, we obtain as combination of the labelings of these cycle parts.