A connected dominating set in a connected graph is a dominating set in whose vertices induce a connected subgraph, i.e., one in which there is no dominating vertex not connected to some other dominating vertex by an edge. Connected dominating sets therefore comprise a subset of all dominating sets in a graph.

A minimum connected dominating set of a graph is a connected dominating set of smallest possible size, where the minimum size is denoted and known as the connected domination number.