Department of Mathematics Gulbarga University Gulbarga Karnataka India

Email:-mhmuddebihal@yahoo.co.in

Let be a connected graph. The litact graph m(G) of a graph G is the graph whose vertex set is the union of the set of edges and the set of cut vertices of G in which two vertices are adjacent if and only if the corresponding members of G are adjacent or incident. A dominating set D of m (G) is called a connected dominating set of m (G) if the induced subgraph is connected. The minimum cardinality of D is called the connected domination number of m (G) and is denoted by . In this paper, we initiate a study of this parameter. We obtain many bonds on in terms of vertices, edges and different parameters of G and not the members of m (G). Further we determine its relationship with other domination parameters.