Total edge irregularity strength of generalized prism

Abstract

The generalized prismPnm can be defined as the Cartesian product Cn□Pm of a cycle on n vertices with a path on m vertices. An edge irregular total k-labeling of a graph G is such a labeling of the vertices and edges with labels 1,2,…,k that the weights of any two different edges are distinct, where the weight of an edge is the sum of the label of the edge itself and the labels of its two end vertices. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength, tes(G).In this paper we determine the exact value of the total edge irregularity strength of the generalized prism Pnm.