On the edge irregular reflexive labeling of corona product of graphs with path

Abstract

We define a total k-labeling (Formula presented.) of a graph G as a combination of an edge labeling (Formula presented.) and a vertex labeling (Formula presented.) such that (Formula presented.) if (Formula presented.) and (Formula presented.) if (Formula presented.) where (Formula presented.) The total k-labeling (Formula presented.) is called an edge irregular reflexive k-labeling of G if every two different edges has distinct edge weights, where the edge weight is defined as the summation of the edge label itself and its two vertex labels. Thus, the smallest value of k for which the graph G has the edge irregular reflexive k-labeling is called the reflexive edge strength of G. In this paper, we study the edge irregular reflexive labeling of corona product of two paths and corona product of a path with isolated vertices. We determine the reflexive edge strength for these graphs.