Irregularity Strength of Corona of Two Graphs

Abstract

Let \(G=(V,E)\) be a connected graph of order \(n\ge 3.\) Let \(f:E\rightarrow \{1, 2,...,k\}\) be a function and let the weight of a vertex v be defined by \(\omega (v)= \sum \limits _{v \in V} f(v)\). Then f is called an irregular labeling if all the vertex weights are distinct. The irregularity strength s(G) is the smallest positive integer k such that there is an irregular labeling \(f:E\rightarrow \{1, 2,...,k\}\). In this paper we determine the irregularity strength of corona \(G \circ H\) where \(G=P_n\) or \(C_n\) and \(H=mK_1\) or \(K_2\) or \(K_3\).