Various Types Of Face Labeling On Different Graphs

Abstract

Face labeling is a specialized graph labeling technique used to assign numerical or symbolic values to the faces of planar graphs while maintaining specific mathematical constraints. It is widely applied in network optimization, circuit design, cybersecurity, and wireless communication. This study explores various types of face labeling, including harmonic, magic, prime, and L(2,1)-face labeling, analysing their theoretical foundations, applications, and optimization strategies. A systematic literature review approach is used to compare labeling techniques and their impact on network performance, resource allocation, and computational efficiency. The study also examines key theorems and mathematical models governing face labeling, highlighting research gaps and future directions. As graph-based applications evolve, integrating face labeling with IoT, AI-driven networks, and large-scale data processing presents opportunities for further advancements.