  Let $G$ be a simple graph of order n. The domination polynomial of G is the
polynomial D(G,x) =\sum d(G, i)x^i, where d(G,i) is the number of dominating
sets of G of size i. Every root of D(G,x) is called the domination root of G.
It is clear that (0,\infty) is zero free interval for domination polynomial of
a graph. It is interesting to investigate graphs which have complex domination
roots with positive real parts. In this paper, we first investigate complexity
of the domination polynomial at specific points. Then we present and
investigate some families of graphs whose complex domination roots have
positive real part.
