Department of Studies and Research in Mathematics Gulbarga University Gulbarga India

Email:- mhmuddebihal@yahoo.co.in Email:- swati.kalshetti@gmail.com

For any graphG , the lict graph nG  J of a graph G is the graph whose vertex set is the union of the set of edges and set of cut vertices of G in which two vertices are adjacent if and only if corresponding members are adjacent or incident. A dominating set D is called connected dominating set of nG , if D is also connected, the minimum cardinality of D is called connected domination number of nG and is denoted by   nc  G . In this paper, many bounds on  nc  G were obtained in terms of vertices, edges and other different parameters of G but not in terms of elements of J .Further we develop its relation with other different domination parameters.