  In this paper we generalize the binary coding procedure of perfect matchings
from catacondensed benzenoid graphs to catacondensed even ring systems (also
called cers). Next, we study cers with isomorphic resonance graphs. For this
purpose, we define resonantly equivalent cers. Finally, we investigate cers
whose resonance graphs are isomorphic to the resonance graphs of catacondensed
benzenoid graphs. As a consequence we show that for each phenylene there exists
a catacondensed benzenoid graph such that their resonance graphs are
isomorphic.
