  We construct a graph TQFT for the minus flavor of Heegaard Floer homology.
Our graph TQFT extends Ozsv\'{a}th and Szab\'{o}'s TQFT for closed and
connected 3-manifolds, and allows for cobordisms with disconnected ends. As an
application, we give an explicit formula for the chain homotopy type of the
$\pi_1$-action on Heegaard Floer homology. We show that on homology the
$\pi_1$-action is trivial on the plus, minus and infinity flavors, but give
examples where it is non-trivial on the hat flavor.
