  In this paper, we study the notions of connected domination number and of
outer-connected domination number for middle graphs. Indeed, we obtain tight
bounds for this number in terms of the order of the graph M(G). We also compute
the outer-connected domination number of some families of graphs such as star
graphs, cycle graphs, wheel graphs, complete graphs, complete bipartite graphs
and some operation on graphs, explicitly. Moreover, some Nordhaus-Gaddum-like
relations are presented for the outer-connected domination number of middle
graphs.
