SOME PAIR DIFFERENCE CORDIAL 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 − ∆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

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2. 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.