Hamiltonian Graph Theory Using Multiplicative Matrix Square Divisor Cordial Labeling for Complex Network Structures

Abstract

Recently, networks have become increasingly complex, requiring advanced mathematical solutions to optimize communication. This paper proposes a mathematical solution for complex network structures based on Hamiltonian Graph Theory (HGT) and Multiplicative Matrix Square Divisor Cordial Labeling (MMSDCL) models. Graph theory provides a framework for representing and analyzing networks, with graph-theoretic measures characterizing the network structure. The proposed model improves network construction performance and offers a redundant solution for finding the least distance to connect network nodes for optimal communication. Compared to previous graph theory models, the proposed solution simplifies network connections, enhancing network communication. Mathematical models of complex networks aid in designing efficient algorithms for routing traffic and reducing complex network structures.