Abstract
Nanostructures tend to comprise distinct and measurable forms, which can be referred to in this context as nanopatterns. Far from being random, these patterns reflect the order of well-understood chemical and physical laws. Under the aegis of said physical and chemical laws, atoms and molecules coalesce and form discrete and measurable geometric structures ranging from repeating lattices to complicated polygons. Rules from several areas of pure mathematics such as graph theory can be used to analyze and predict properties from these well-defined structures. Nanocarbons have several distinct allotropes that build upon the basic honeycomb lattice of graphene. Because these allotropes have clear commonalities with respect to geometric properties, this paper reviews some approaches to the use of graph theory to enumerate structures and potential properties of nanocarbons. Graph theoretic treatment of the honeycomb lattice that forms the foundation of graphene is completed, and parameters for further analysis of this structure are analyzed. Analogues for modelling graphene and potentially other carbon allotropes are presented.
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Fagnan, E., Cormia, R. Graph-Theoretic Analysis of Nanocarbon Structures. MRS Advances 1, 1761–1766 (2016). https://doi.org/10.1557/adv.2016.113
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DOI: https://doi.org/10.1557/adv.2016.113