On d-antimagic labelings of antiprisms

Abstract

This paper deals with d-antimagic labeling of antiprisms. In a d-antimagic labeling the vertices, edges and faces of a plane graph are labeled 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 the face and the weights of faces constitute an arithmetical progression of difference d. In this paper we prove that for n ≥ 5, the antiprism A_n is d-antimagic of type (1,1,1) for d = 3, 5 and 6.