  We prove that the fundamental group of a finite graph of convergence groups
with parabolic edge groups is a convergence group. Using this result, under
some mild assumptions, we prove a combination theorem for a graph of
convergence groups with dynamically quasi-convex edge groups (Theorem 1.3). To
prove these results, we use a modification of Dahmani's technique [Dah03]. Then
we show that the fundamental group of a graph of relatively hyperbolic groups
with edge groups either parabolic or infinite cyclic is relatively hyperbolic
and construct Bowditch boundary. Finally, we show that the homeomorphism type
of Bowditch boundary of the fundamental group of a graph of relatively
hyperbolic groups with parabolic edge groups is determined by the homeomorphism
type of the Bowditch boundaries of vertex groups (under some additional
hypotheses)(Theorem 7.1). In the last section of the paper, we give some
applications and examples.
