Let G be a simple graph. A set  is called a connected dr-power dominating set of Gif it is a dr-power dominating set and the induced subgraph of P, denoted by  is connected. The minimum cardinality of a connected dr-power dominating set Pof a graph G, denoted by  is the connected dr-power domination number of G. This parameter is at most equal to the connected domination number of a graph G. In this paper, we investigate the connected dr-power dominating sets in a graph. It is shown that any two positive integers aand b, where  are realizable as the connected dr-power domination number and connected domination number, respectively. Connected dr-power dominating sets in the join, corona, and lexicographic product of graphs are also characterized.

connected domination, dr-power domination, directly observed vertex, remotely observed vertex, directly observed edge, remotely observed edge, connected dr power domination.