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 $K_3$.