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Diameter of nanotori

Author

Listed:
  • Andova, Vesna
  • Dimovski, Pavel
  • Knor, Martin
  • Škrekovski, Riste

Abstract

A cubic graph which has only hexagonal faces, and can be embedded into a torus is known as generalized honeycomb torus or honeycomb toroidal graph, abbreviated as nanotorus. This graph is determined by three parameters a,b, and c, and denoted by Ga,b,c. B. Alpspach in 2010 dedicated a survey paper to nanotori, wherein a number of open problems are suggested. In this article we deal with one of the problems given in the survey to determine the diameter of nanotorus Ga,b,c as a function of the parameters a,b, and c. We obtain that the diameter of Ga,b,c for b≤a is just a. For the case a

Suggested Citation

  • Andova, Vesna & Dimovski, Pavel & Knor, Martin & Škrekovski, Riste, 2024. "Diameter of nanotori," Applied Mathematics and Computation, Elsevier, vol. 462(C).
    • Handle: RePEc:eee:apmaco:v:462:y:2024:i:c:s0096300323005118
    DOI: 10.1016/j.amc.2023.128342
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    References listed on IDEAS

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    1. R. C. Haddon, 1997. "Electronic properties of carbon toroids," Nature, Nature, vol. 388(6637), pages 31-32, July.
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    1. Vesna Andova & Pavel Dimovski & Martin Knor & Riste Škrekovski, 2020. "On Three Constructions of Nanotori," Mathematics, MDPI, vol. 8(11), pages 1-16, November.

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