Pair difference cordiality of some graphs derived from ladder graph

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 behaviour of some graphs like slanting ladder SL_n, mobius ladder M_n, triangular ladder TL_n.