Pair difference cordial labeling of graphs

Abstract

Let G = (V,E) be a (p,q) graph. Define ρ = p/2, if p is even; (p−1)/2, if p is odd; and L = {±1,±2,±3,··· ,±ρ} 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 −∆f₁^c| ≤ 1, where ∆f₁ and ∆f₁^c respectively 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 path, cycle, star, comb.