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Resonance graphs of catacondensed even ring systems

Author

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  • Brezovnik, Simon
  • Tratnik, Niko
  • Žigert Pleteršek, Petra

Abstract

A catacondensed even ring system (shortly CERS) is a simple bipartite 2-connected outerplanar graph with all vertices of degree 2 or 3. In this paper, we investigate the resonance graphs (also called Z-transformation graphs) of CERS and firstly show that two even ring chains are evenly homeomorphic iff their resonance graphs are isomorphic. As the main result, we characterize CERS whose resonance graphs are daisy cubes. In this way, we greatly generalize the result known for kinky benzenoid graphs. Finally, some open problems are also presented.

Suggested Citation

  • Brezovnik, Simon & Tratnik, Niko & Žigert Pleteršek, Petra, 2020. "Resonance graphs of catacondensed even ring systems," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    • Handle: RePEc:eee:apmaco:v:374:y:2020:i:c:s0096300320300333
    DOI: 10.1016/j.amc.2020.125064
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    References listed on IDEAS

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    1. Črepnjak, Matevž & Tratnik, Niko, 2017. "The Szeged index and the Wiener index of partial cubes with applications to chemical graphs," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 324-333.
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