### Pair difference cordial labeling of 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_{1}^{c}| ≤ 1, where ∆f_{1} and ∆f_{1}^{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 behavior of path, cycle, star, comb.

**Published:**2021-04-05

**How to Cite this Article:**R. Ponraj, A. Gayathri, S. Somasundaram, Pair difference cordial labeling of graphs, J. Math. Comput. Sci., 11 (2021), 2551-2567 Copyright © 2021 R. Ponraj, A. Gayathri, S. Somasundaram. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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