Face antimagic labelings of prisms

Abstract

This 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 labels of vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph 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 d-antimagic labelings for prism for d ∈ {7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 24, 26, 27, 30, 36}.