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arXiv · 1906.06111

On the Djokovi\'c-Winkler relation and its closure in subdivisions of fullerenes, triangulations, and chordal graphs

Sandi Klavžar·Kolja Knauer·Tilen Marc
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Abstract

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 Djokovi\'c-Winkler relation $\Theta$ and its transitive closure $\Theta^\ast$. In this paper we study the behavior of $\Theta$ and $\Theta^\ast$ with respect to full subdivisions. We apply our results to describe $\Theta^\ast$ in full subdivisions of fullerenes, plane triangulations, and chordal graphs.

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Sandi Klavžar, Kolja Knauer, Tilen Marc. 2019-06-14. On the Djokovi\'c-Winkler relation and its closure in subdivisions of fullerenes, triangulations, and chordal graphs. https://arxiv.org/abs/1906.06111

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