Basic Minimal Total Dominating Functions of Quadratic Residue Cayley Graphs

Domination theory is an important branch of Graph Theory and has many applications in Engineering, Communication Networks and many others. Allan, R.B., and Laskar, R., [1,2], Cockayne, E.J.,and Hedetniemi, S.T., [3], Haynes, T.W., and Slater, J.S., [4], have studied various domination parameters of graphs. Graphs associated with certain arithmetic functions which are usually called arithmetic graphs have been studied extensively by many researchers. In this paper we study the minimal total dominating functions and basic minimal total dominating functions (BMTDFs) of quadratic residue Cayley graphs and results on these functions are obtained. The theory of BMTDFs in quadratic residue Cayley graphs is an impulsive and methodical program that provides numerous interesting theoretical and computational aspects. It helps to study the related theory in other classes of graphs for further research and also improves the ability of work in some networks such as telecommunications, mobile applications etc.