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Resonance graphs of catacondensed even ring systems are median

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
253
Identifiers
DOI: 10.1016/s0012-365x(01)00447-2
Keywords
  • Benzenoid Graph
  • Median Graph
  • Resonance Graph
  • 1-Factor
  • Z-Transformation Graph
  • Convex Expansion
Disciplines
  • Chemistry

Abstract

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.

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