Pair mean cordial labeling of diamond snake graph, banana tree and tortoise graph

Abstract

Let a graph G = (V, E) be a (p, q) graph. Define ρ = { p/2 p is even p−1/2 p is odd, and M = {±1, ±2, · · · ± ρ} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M 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 mean cordial labeling if for each edge uv of G, there exists a labeling λ(u)+λ(v)/2 if λ(u) +λ(v) is even and λ(u)+λ(v)+1/2 if λ(u) +λ(v) is odd such that |S¯λ1 −S¯λc1| ≤ 1 where S¯λ1 and S¯λc1 respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G with a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of the diamond snake graph, banana tree, tortoise graph and generalized web graph without the central vertex.