EXPLORING THE IMPACT OF DOMINATION IN GRAPH STRUCTURES: A COMPREHENSIVE STUDY - Warad, Nanda S; Begum, Faimida (ShodhKosh: Journal of Visual and Performing Arts, 2024)
Graph domination is a key concept in graph theory, with wide-ranging applications in network security, social networks, and biological systems. This paper presents a comprehensive study of domination in graph structures, exploring various types of domination such as total domination, independent domination, and connected domination. The study delves into the theoretical foundations of domination, including critical bounds, domination numbers, and their computational complexity. The paper also examines real-world applications, highlighting how domination plays a crucial role in optimizing network communication, sensor placement, and resource management. Additionally, we analyze algorithmic approaches for calculating domination numbers and explore how domination impacts graph connectivity and stability in practical scenarios. The results provide insights into how domination theory can be leveraged to enhance the performance and efficiency of complex networks.