  A vertex subset $W\subseteq V$ of the graph $G=(V,E)$ is an independent
dominating set if every vertex in $V\backslash W$ is adjacent to at least one
vertex in $W$ and the vertices of $W$ are pairwise non-adjacent. The
independent domination polynomial is the ordinary generating function for the
number of independent dominating sets in the graph. We investigate in this
paper properties of the independent domination polynomial and some interesting
connections to well known counting problems.
