  We investigate combinatorial aspects of exceptional sequences in the derived
category of coherent sheaves on certain smooth and complete algebraic surfaces.
We show that to any such sequence there is canonically associated a complete
toric surface whose torus fixpoints are either smooth or cyclic T-singularities
(in the sense of Wahl) of type $\frac{1}{r^2}(1, kr - 1)$. We also show that
any exceptional sequence can be transformed by mutation into an exceptional
sequence which consists only of objects of rank one.
