Resonance Graphs and a Binary Coding for the 1-Factors of Benzenoid Systems

Applying the recently obtained distributive lattice structure on the set of 1-factors, we show that the resonance graphs of any benzenoid systems G, as well as of general plane (weakly) elementary bipartite graphs, are median graphs and thus extend greatly KlavŽar et al.'s result. The n-dimensional vectors of nonnegative integers as a labelling for the 1-factors of G with n inner faces are described. The labelling preserves the partial ordering of the above-mentioned lattice and can be transformed into a binary coding for the 1-factors. A simple criterion for such a labelling being binary is given. In particular, KlavŽar et al.'s algorithm is modified to generate this binary coding for the 1-factors of a cata-condensed benzenoid system.