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Finding the hole in a wall

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Abstract

In this paper we model a graphene nano-ribbon structure by analysing an infinite 3-regular hexagonal grid which is transformed to a rectangular coordinate system or “wall”. Our goal is to solve the inverse problem of identifying the position of a single vacancy break using the lengths of the closed paths along the edges of the underlying graph. We provide an algorithm to determine the exact position of the defect by using data from at most three reference points.

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Funding

This material is based upon work supported by the National Research Foundation under Grant Numbers 89147 and 103530.

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Authors and Affiliations

  1. School of Mathematics, University of the Witwatersrand, Private Bag 3, P O WITS, Johannesburg, 2050, South Africa

    M. Archibald & S. Currie

  2. Faculty of Applied Mathematics, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059, Krakow, Poland

    M. Nowaczyk

Authors
  1. M. Archibald
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  2. S. Currie
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  3. M. Nowaczyk
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Correspondence to S. Currie.

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Archibald, M., Currie, S. & Nowaczyk, M. Finding the hole in a wall. J Math Chem 58, 2313–2323 (2020). https://doi.org/10.1007/s10910-020-01178-3

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  • DOI: https://doi.org/10.1007/s10910-020-01178-3

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