PAIR MEAN CORDIAL LABELING OF CERTAIN LADDER GRAPHS

PAIR MEAN CORDIAL LABELING OF CERTAIN LADDER GRAPHS

Consider a (p, q) graph G = (V, E). Define $${\varrho}=\begin{cases}{\frac{p}{2}} & p\;{\text{is even}}\\{\frac{p-1}{2}} & p\;{\text{is odd}},\end{cases}$$ and Υ = {±1, ±2, . . ., ±ϱ} referred to as the label set. Let us consider a mapping 𝜑 : V → Υ, where, for every even p, distinct labels are assigned to the various elements of V in Υ, and for every odd p , distinct labels are assigned to the p - 1 elements of V in Υ, with a repeating label for the remaining one vertex. After that 𝜑 is referred to as a pair mean cordial labeling (PMC-labeling) if for every edge 𝜇𝜈 in G, there is a label for $\frac{{\varphi}({\mu})+{\varphi}({\nu})}{2}$ if 𝜑(μ) + 𝜑(ν) is even and $\frac{{\varphi}({\mu})+{\varphi}({\nu})+1}{2}$ if 𝜑(μ) + 𝜑(ν) is odd such that ${\mid}{\bar{\mathbb{S}}}_{{\varphi}_1}-{\bar{\mathbb{S}}}_{{\varphi}^c_1}{\mid}\,{\leq}1$ where ${\bar{\mathbb{S}}}_{{\varphi}_1}$ and ${\bar{\mathbb{S}}}_{{\varphi}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1 respectively. A pair mean cordial graph (PMC-graph) is defined as a graph G with PMC-labeling. In this paper, we investigate the pair mean cordial labeling behavior of open ladder, triangular ladder, diagonal ladder, slanting ladder, circular ladder and diamond ladder.