Resonance graphs of catacondensed even ring systems are median

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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 Qf, where / is the number of bounded faces of G. ©2002 Elsevier Science B.V. All rights reserved.

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Klavzar, S., Zigert, P., & Brinkmann, G. (2002). Resonance graphs of catacondensed even ring systems are median. Discrete Mathematics, 253(1–3), 35–43. https://doi.org/10.1016/S0012-365X(01)00447-2

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