In this paper we establish a connection between ribbon graphs and Brauer graphs. As a
result, we show that a compact oriented surface with marked points gives rise to a unique
Brauer graph algebra up to derived equivalence. In the case of a disc with marked points we
show that a dual construction in terms of dual graphs exists. The rotation of a diagonal in an
m-angulation gives rise to a Whitehead move in the dual graph, and we explicitly construct a
tilting complex on the related Brauer graph algebras reflecting this geometrical move.