A Study on Domination Parameters of Graphs

Domination in graphs is an important concept in Graph Theory and network analysis. It focuses on identifying a subset of vertices that can effectively control or monitor the entire graph. Domination parameters such as domination number, total domination number,connected domination number, and independent domination number play a crucial role in analysing the structural properties of graph networks. These parameters have numerous applications in wireless sensor networks, communication systems, facility location problems,
and social network analysis. This Chapter presents an overview of domination parameters in graph networks, discusses their mathematical definitions, and explains their significance in network optimization. The study also explores different domination models and their theoretical implications in modern graph-based systems.Understanding these domination parameters helps in designing efficient algorithms for monitoring, controlling, and optimizing large-scale networks.