  Circular-arc graphs are intersection graphs of arcs on the circle. The aim of
our work is to present a polynomial time algorithm testing whether two
circular-arc graphs are isomorphic. To accomplish our task we construct
decomposition trees, which are the structures representing all normalized
intersection models of circular-arc graphs. Normalized models reflect the
neighbourhood relation in circular-arc graphs and can be seen as their
canonical representations; in particular, every intersection model can be
easily transformed into a normalized one.
  Our work adapts and appropriately extends the previous work on the similar
topic done by Hsu [\emph{SIAM J. Comput. 24(3), 411--439, (1995)}]. In his
work, Hsu developed decomposition trees representing all normalized models of
circular-arc graphs. However due to the counterexample given in [\emph{Discrete
Math. Theor. Comput. Sci., 15(1), 157--182, 2013}], his decomposition trees can
not be used by algorithms testing isomorphism of circular-arc graphs.
