  We find numerical and empirical evidence for dynamical, structural and
topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in
the temporal vicinity of the worldwide financial crash. Using the Minimal
Spanning Tree (MST) technique, a particularly useful canonical tool of the
graph theory, two transitions of the topology of a complex network representing
FSE were found. First transition is from a hierarchical scale-free MST
representing the stock market before the recent worldwide financial crash, to a
superstar-like MST decorated by a scale-free hierarchy of trees representing
the market's state for the period containing the crash. Subsequently, a
transition is observed from this transient, (meta)stable state of the crash, to
a hierarchical scale-free MST decorated by several star-like trees after the
worldwide financial crash. The phase transitions observed are analogous to the
ones we obtained earlier for the Warsaw Stock Exchange and more pronounced than
those found by Onnela-Chakraborti-Kaski-Kert\'esz for S&P 500 index in the
vicinity of Black Monday (October 19, 1987) and also in the vicinity of January
1, 1998. Our results provide an empirical foundation for the future theory of
dynamical, structural and topological phase transitions on financial markets.
