Optimizing Network Structures Through Neutrosophic Graph Product Operations and its Coloring: A Comprehensive Approach for Enhanced Connectivity and Robustness

作     者：Meenakshi, A. Dhanushiya, S. 

作者机构：Department of Mathematics Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Chennai600 062 India 

出 版 物：《Neutrosophic Sets and Systems》 (Neutrosophic Sets Syst.)

年 卷 期：2025年第76卷

页      面：400-429页

核心收录：

主　　题：Network theory (graphs) 

摘      要：Optimal network analysis requires advanced techniques to handle the inherent complexity and uncertainty of real-world systems. We have used vertex order coloring on neutrosophic graphs to find the most effective approach to improve network reliability and performance. Neutrosophic graphs( ) offer a comprehensive framework for modelling real-world networks with inherent uncertainties by incorporating degrees of truth, falsity, and indeterminacy. In this paper, we have investigated various graph product operations as a means of optimizing network structures. We further investigated the applications of vertex order coloring to identify and strong vertices within various graph operations of . We examined several products with the goal of determining the most optimal network based on particular important metrics including the total number of alpha-strong vertices, the weight of alpha-strong vertices, the chromatic number, and the weight of the graph s minimum spanning tree. The objective of our research is to identify the best solutions that strike a balance between robustness and association by rigorously studying and comparing various product operations. Our research advances the subject of network theory and provides useful information for a variety of applications, including social networks, transportation, and telecommunications. © 2025, University of New Mexico. All rights reserved.