The connected domination number of a connected graph ,
denoted
,
is the size of a minimum connected
dominating set of a graph
.
The maximum leaf number and connected domination number of a graph
are connected by
where
is the vertex count of
.
It is NP-complete to test if there exists a connected dominating set having size less than some given value.
Many families of graphs have simple closed forms, as summarized in the following table. In the table, denotes the floor function.