SOME PAIR DIFFERENCE CORDIAL GRAPHS

Year 2021, Volume: 3 Issue: 2, 17 - 26, 10.10.2021

R Ponraj , Gayathrı A , S Somasndaram

https://doi.org/10.54286/ikjm.926656

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 − ∆f
c
1


 ≤ 1,
where ∆f1
and ∆f
c
1
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
Pn ⊙ K1,Pn ⊙ K2,Cn ⊙ K1,Pn ⊙ 2K1,Ln ⊙ K1,Gn ⊙ K1, where Gn is a gear
graph and e

Keywords

path, cycle, complet graph, ladder

References

• 1. Prajapati, U.M., and Gajjar, S.J., Cordial labeling for complement graphs,Mathematics TodayVol.30, (2015), 99–118.
• 2. Prajapati, U.M., and Gajjar, S.J., Some results on prime cordial labeling of generalized prism graph Ym,n,Ultra ScientistVol.27(3)A, (2015), 189–204.