Department of Mathematics, Gulbarga University, Gulbarga, 585106, (INDIA)

Email of Corresponding author :- E-mail: vrkulli@gmail.com

Let G = (V, E) be a graph. Let D be a minimum secure dominating set of G. If V – D contains a secure total dominating set D’ of G, then D’ is called an inverse secure dominating set with respect to D. The smallest cardinality of inverse secure dominating set of G is the secure domination number s -1(G) of G. In this paper, we obtain some graphs for which s(G) = s -1(G) and establish some results on this respect. Also we obtain some graphs for which s(G) =s -1(G) = 2 . p where p is the number of vertices of G.