Resonance graphs of catacondensed even ring systems are median

Abstract

Let G be a planar embedded 2-connected graph. Then the vertices of its resonance graph R( G) are the 1-factors of G, two 1-factors being adjacent whenever their symmetric difference is a bounded face of G. For a class of graphs containing the chemically important catacondensed benzenoid graphs we show that the resonance graphs are median. In particular, if G belongs to this class, R( G) has an isometric embedding into Q f , where f is the number of bounded faces of G.