PAIR MEAN CORDIAL LABELING SOME FAMILIES OF SPECIAL GRAPHS

Abstract

In this paper we study Pair Mean Cordial (PMC) labeling is type of graph labeling in which each edge receives a label determined by the mean (average) of the integer labels assigned to its endpoints and the resulting edge labels are distributed as evenly as possible. We investigate the existence of PMC-labeling for several well-known special graphs like gear graphs, bistar graphs, book graphs, barbell graphs, and their unions. For each class, we determine necessary and sufficient conditions under which a PMC-labeling exists, and provide constructions or counterexamples accordingly. We also examine how the PMC-property behaves under union operations and identify criteria that preserve cordiality.