In contemporary research, graph theory serves as a versatile tool for analyzing and optimizing various aspects of interconnection networks. This multidisciplinary approach delves into parameters like the co-secure domination number, topological indices, detour eccentric sums of graphs, and k-fault power domination, shedding light on the practical implications of these investigations. The co-secure domination number is an essential metric for enhancing network security. It identifies the minimum number of nodes required to secure a network against unauthorized access or data breaches. Understanding this number aids in deploying resources efficiently for safeguarding sensitive information and critical systems in interconnected networks. Topological indices are another area of study, offering insights into the structure and performance of interconnected systems. By examining these indices, researchers can identify vulnerabilities, optimize network design, and enhance information flow, ultimately improving the overall efficiency and reliability of interconnection networks. Detour eccentric sums of graphs are a vital parameter in network analysis, helping to reveal how interconnected nodes interact and contribute to the overall functioning of a network. Understanding the eccentricity of nodes through detours provides a more comprehensive perspective on network dynamics, guiding decisions related to routing, data transmission, and resource allocation. K-fault power domination explores network robustness in the face of component failures. It offers solutions to enhance fault tolerance, making interconnection networks more resilient against unforeseen disruptions, which is particularly crucial in critical infrastructure and communication systems. The practical applications of these parameters are manifold. From securing data and critical infrastructure to optimizing network performance, these studies have the potential to significantly impact the real-world operation of interconnection networks, ultimately leading to more reliable, secure, and efficient interconnected systems.