Domination Properties of Honeycomb Rhombic Graph

Abstract

A dominating number of a graph is the order of the smallest dominating set in the graph. The minimum weight of all possible Roman dominating functions on a graph is called the Roman dominating number. A Honeycomb rhombic graph is a 3-regular graph. Recent research explains the benefits of Honeycomb rhombic structure in many applications, like network analysis, biomedicine, sensor analysis, chemistry and many more. The main objective is to find the domination number and Roman domination number for the Honeycomb rhombic graph. Our results provide a deeper perception of efficient coverage and being a system control mechanisms in Honeycomb rhombic network.