  A polynomial is said to be unimodal if its coefficients are non-decreasing
and then non-increasing. The domination polynomial of a graph $G$ is the
generating function of the number of domination sets of each cardinality in
$G$, and its coefficients have been conjectured to be unimodal. In this paper
we will show the domination polynomial of paths, cycles and complete
multipartite graphs are unimodal, and that the domination polynomial of almost
every graph is unimodal with mode $ \lceil \frac{n}{2}\rceil $.
