PAIR DIFFERENCE CORDIAL LABELING OF SOME UNION OF GRAPHS

PAIR DIFFERENCE CORDIAL LABELING OF SOME UNION OF GRAPHS

R. Ponraj, A. Gayathri, S. Somasundaram

[PDF]

Abstract

Let G = (V, E) be a (p, q) graph. Define 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 ele- ments 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 − ∆f1c ≤ 1, where ∆f1 and ∆f1c 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 the union of some graphs like path, cycle, star and bistar graph.

Keywords

Path, star, cycle, bistar, comb, fan.