Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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PAIR DIFFERENCE CORDIAL LABELING OF PETERSEN GRAPHS P(n, k)

  • R. PONRAJ (Department of Mathematics, Sri Paramakalyani College) ;
  • A. GAYATHRI (Department of Mathematics, Manonmaniam Sundaranar University) ;
  • S. SOMASUNDARAM (Department of Mathematics, Manonmaniam Sundaranar University)
  • Received : 2022.10.23
  • Accepted : 2023.01.13
  • Published : 2023.03.30
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Abstract

Let G = (V, E) be a (p, q) graph. Define $${\rho}=\{{\frac{2}{p}},\;{\text{{\qquad} if p is even}}\\{\frac{2}{p-1}},\;{{\text{if p is odd}}$$ 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 ${\mid}{\Delta}_{f_1}-{\Delta}_{f^c_1}{\mid}{\leq}1$, where ${\Delta}_{f_1}$ and ${\Delta}_{f^c_1}$ 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 pair difference cordial labeling behaviour of Petersen graphs P(n, k) like P(n, 2), P(n, 3), P(n, 4).

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Acknowledgement

The authors thank the Referee for their valuable suggestions towards the improvement of the paper.

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