Analysis of PMC-Labeling in Certain Graph Structures

This paper presents an investigation of pair mean cordial (PMC) labeling for several classes of special graphs, including the torus grid graph, king graph, generalized key graph, generalized Petersen graph, double triangular snake, and double alternate triangular snake. The existence of PMC-labeling for these graph structures is established through suitable constructions and labeling techniques. The study is further motivated by its potential applications in network-related problems, where graph labeling plays a significant role in efficient resource allocation, frequency assignment, and communication channel distribution. In particular, PMC-labeling helps achieve near-balanced edge labeling, which can be effectively utilized in designing communication networks with minimal interference and balanced load distribution.