PAIR MEAN CORDIAL LABELING OF GRAPHS OBTAINED FROM PATH AND CYCLE

Let a graph G = (V, E) be a (p, q) graph. Define <TEX>$${ ho};=;{array{{frac{p}{2}}&p ext{ is even}\{frac{p-1}{2}};&p ext{ is odd,}}$$</TEX> and M = {&#x00B1;1, &#x00B1;2, &#x22EF; &#x00B1; &#x1D70C;} called the set of labels. Consider a mapping &#x03BB; : &#x0056; &#x2192; 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 <TEX>$frac{{lambda}(u)+{lambda}(v)}{2}$</TEX> if &#x03BB;(u) + &#x03BB;(v) is even and <TEX>$frac{{lambda}(u)+{lambda}(v)+1}{2}$</TEX> if &#x03BB;(u) + &#x03BB;(v) is odd such that <TEX>${mid}ar{mathbb{S}}_{{lambda}_1}-ar{mathbb{S}}_{{lambda}^c_1}{mid}{leq}1$</TEX> where <TEX>$ar{mathbb{S}}_{{lambda}_1}$</TEX> and <TEX>$ar{mathbb{S}}_{{lambda}^c_1}$</TEX> respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling of graphs which are obtained from path and cycle.