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.
