Modular irregularity strength of the corona product of graphs

Let G(V, E) be a graph of order n.A modular irregular labeling of G is an edge k-labeling φ : E(G) → {1, 2, . . ., k} provided that the weight function σ :, where E(u) denotes the set of all those edges in E(G) that are incident with the vertex u and Zn is the group of integers modulo n.This weight function is called a modular weight of the vertex u.The minimum number k such that the graph G has a modular irregular labeling with the largest label k is called the modular irregularity strength of G.In this paper, we determine the modular irregularity strength of the corona product of a graph G with the edgeless graph of order p (that is, the graph consisting of p isolated vertices) and with the path graph P3 of order 3, where G is a regular graph containing a 1-factor.