Computer Network Access Codes with Various Types of Network Design by Using Dominant Local Resolving Set Theory

Abstract

Computer networks spanning multiple buildings face increasing challenges in efficient access control, optimal server placement, and rapid fault identification. As network structures grow more complex, there is a strong motivation to develop a mathematical framework that minimizes resource usage while ensuring full network coverage and unique node identification. This study addresses these challenges by applying dominant local resolving set theory to computer network design.The methodology adopts an axiomatic–deductive approach, modeling computer networks as connected graphs where devices are represented by vertices and communication links by edges. The analysis focuses on dominant local metric dimensions of standard graph families and vertex amalgamation products, which effectively model heterogeneous multi-building network topologies. A structured framework is developed to determine dominant local bases and corresponding access codes.The most significant results establish exact formulas for the dominant local metric dimension of vertex amalgamation graphs. The results show that this dimension is determined by the dominant local metric dimensions of the constituent graphs and is strongly influenced by the choice of linkage vertices, with reductions occurring under specific modular conditions.These findings demonstrate the broader significance of dominant local resolving set theory in designing cost-effective and scalable computer networks. The proposed framework provides practical guidance for minimizing the number of service providers, improving fault diagnosis, and optimizing access code assignment in complex distributed network environments.