The Domination Parameters on a kind of the regular honeycomb structure

The honeycomb mesh, based on hexagonal structure, has enormous applications in chemistry and engineering. A major challenge in this field is to understand the unique properties of honeycomb structures, which depend on their properties of topology. One of the important concepts in graph theory is the domination number which can be used for network control and monitoring. In this paper, we investigate the domination number of the honeycomb network. For this purpose, the domination number, the total domination number, the independent domination number, the connected domination number and the doubly connected domination number of the honeycomb are obtained. Finally, in some honeycomb structures of real models, we obtain the exact amount of these parameters.