Graph Theoretical Analysis of Roman Domination in Metal-Organic Networks

Abstract

Roman domination theory, a significant area within graph theory, examines the concept of domination in graphs through the framework of Roman dominating functions. This project investigates the fundamental properties of Roman domination, including the determina- tion of the Roman domination number, denoted by γR(G), which represents the minimum number of vertices needed in a Roman dominating function for a given graph, as well as computation of the domination number γ(G), which represents the minimum number of vertices required to dominate a given graph G. Furthermore, we explore the application of Roman domination theory to the analysis of metal-organic networks MONs, a class of complex chemical structures with diverse applications in materials science, catalysis, and nanotechnology. Using Roman dominating functions, we investigate the efficiency and effectiveness of dominating sets in MONs, aiming to elucidate their structural and compu- tational properties. We study domination number and Roman domination number for the metal-organic networks MONs and the line graph of metal-organic networks MONs.