  In this paper we study relations between connected and weakly convex
domination numbers. We show that in general the difference between these
numbers can be arbitrarily large and we focus on the graphs for which a weakly
convex domination number equals a connected domination number. We also study
the influence of the edge removing on the weakly convex domination number, in
particular we prove that the weakly convex domination number is an
interpolating function.
