Pair difference cordial labeling of some union of graphs

Abstract

Let G = (V, E) be a (p, q) graph. Define ? = {p/2 if p is even p?1/2 if p is odd and L = {±1, ±2, ±3, · · · , ±?} called the set of labels. Consider a mapping f : V ? L by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) ? f(v)| such that ?f1 ? ?fc1 ? 1, where ?f1 and ?fc1respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of the union of some graphs like path, cycle, star and bistar graph.