On the Djoković-Winkler relation and its closure in subdivisions of fullerenes, triangulations, and chordal graphs
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It was recently pointed out that certain SiO_2 layer structures and SiO_2 nanotubes can be described as full subdivisions aka subdivision graphs of partial cubes. A key tool for analyzing distance-based topological indices in molecular graphs is the Djoković-Winkler relation Θ and its transitive closure Θ^∗. In this paper we study the behavior of Θ and Θ^∗ with respect to full subdivisions. We apply our results to describe Θ^∗ in full subdivisions of fullerenes, plane triangulations, and chordal graphs.
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