Mean Edge Cordial Labeling of Path Structured Graphs with Applications

Abstract

Balanced binary edge labeling schemes are established for several families of path structured graphs, including path, comb, fan, double Fan, Z  and square of path graphs. For each graph, explicit constructive labeling schemes are developed and shown to satisfy the required balance conditions on both edge labels and induced vertex labels. The study further presents a dynamic interpretation of these labeling patterns through accessibility regulation and scheduling mechanisms on linear and centrally coordinated network structures. Rotational update strategies and phase-based coordination procedures are shown to produce balanced propagation of operational accessibility among network nodes. These results extend the class of graphs known to admit mean edge cordial labeling and demonstrate the applicability of structural labeling techniques in modeling low-complexity coordination processes in distributed networks.