Super d-Antimagic labelings of disjoint union of generalized prisms

Abstract

The generalized prism, Pmn can be defined as the Cartesian product of a cycle on n vertices with a path on m vertices. In this paper we deal with the problem of labeling the vertices, edges and faces of a disjoint union of r copies of P™ by the consecutive integers starting from 1 in such a way that the set of face-weights of all s-sided faces form an arithmetic progression with common difference d, where by the face-weight we mean the sum of the label of that face and the labels of vertices and edges surrounding that face.