Funct. Mater. 2024; 31 (1): 110-118.

doi:https://doi.org/10.15407/fm31.01.110

A simple topological index for measuring nonbipartivity in nanostructures

A.V. Luzanov

STC "Institute of Single Crystals", National Academy of Sciences of Ukraine, 60 Nauky Ave., 61001 Kharkiv, Ukraine

Abstract:

We consider a nonbipartivity quantification problem for complex atomistic structures treated as graphs. In simple words, the bipartivity means that the corresponding graph has no odd-membered cycles. Based on preliminary results (2021) we now propose a topological index IAS. By the latter a graph spectral asymmetry is suitably transformed into a size-extensive measure of nonbipartivity. The IAS index ls tested on simple graphs, and compared with other nonbipartivity indexes. For several graph types (cycles, sunlet and wheel graphs etc.) the analytical results are obtained. The focus of our numerical computations is on large-scale nanoclusters (fullerenes with hundreds atoms and nonbipartite defects in graphene nanoclusters). It is emphasized that the size-extensivity of the given measure IAS is principal when analyzing nonbipartivity in quantitative terms.

Keywords:

adjacency matrix, parity theorem, cycle-based graphs, vertex frustration, giant fullerenes, nanographenes.

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