Irregularity strength and compound graphs

Abstract

The irregularity strength of a graph G is the smallest possible value of k or which we can assign positive integers not greater than k to the edges of G, in such a way that the sums at each vertex are distinct numbers. In this paper, we study the irregularity strength in relation with a graph composition. We prove a general bound for the irregularity strength of regular compound graphs and derive exact results for some infinite families of graphs.