Diameter of nanotori

Vesna Andova, Pavel Dimovski, Martin Knor and Riste Škrekovski

Applied Mathematics and Computation, 2024, vol. 462, issue C

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 aKeywords: Nanotorus; Diameter; Generalized honeycomb torus; Honeycomb tiroidal graph; Regular maps (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:462:y:2024:i:c:s0096300323005118

DOI: 10.1016/j.amc.2023.128342

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