Redundant Mathematical Solution for Complex Homotopy Structures using Graph Theory based on Bipartite Chromatic Polynomial for Solving Distance Problems

Introduction: Increasing network communication area has lot of unstructured routing to create complex structures. The communication structure is non-linear to create connective edges to degrade the communication performance. Many non-linear solutions and distance theory models contains maximum non-liability of variables are taken to solve the problems. But structure difference and dynamic variables are constantly applied to make solution which leads errors and complex solutions. To resolve this problem, to propose a Redundant mathematical solution for complex homotopy structures using Multinomial-Cordial Graph Theory (MCGT) based on Bipartite Chromatic Polynomial Distribution Theory (BCPDT) for solving distance problems. To apply neighbor-based distance coverage model with cordial labeling variable structure to reduce the complexity variable structure problems, this paper explores a novel strategy for encapsulating the non-linear complex homotopy in its entirety by employing graph theory and the concept of cordial labeling. By establishing a connection between algebraic topology and graph theoretical constructs, we formulate a redundant solution that illuminates the intricacies of complex homotopy but also provides practical methodologies for solving distance-related issues prevalent in various mathematical and applied fields as well, compared to the previous models.