Resonance graphs of catacondensed even ring systems are median

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 Qf , where f is the number of bounded faces of G. Key words: benzenoid graph, median graph, resonance graph, 1-factor, Z-transformation graph, convex expansion

• Type: Journal
• Year: 2002
• Where: DM
• Authors: Sandi Klavzar, Petra Zigert, Gunnar Brinkmann
• Keywords: 2-connected Graph, DM 2002, Resonance Graph, Symmetric Difference