On the Djoković-Winkler relation and its closure in subdivisions of fullerenes, triangulations, and chordal graphs

2019/06/14 by Sandi Klavžar, Klavžar, Sandi, Kolja Knauer +3 · 1 citation
Chemistry · Computer Science · Materials Science · Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Graphene research and applications #Synthesis and Properties of Aromatic Compounds #cs.DM #math.CO

paper · pdf · doi:10.48550/arxiv.1906.06111

13 pages, 5 figures, fixed a bug in Lemma 4.1

openalex publication_date 2019/06/14 · openalex created_date 2019/06/27 · arxiv created 2020/08/13 · arxiv updated 2020/08/14 · openalex updated_date 2026/07/28

Abstract

It was recently pointed out that certain SiO₂ layer structures and SiO₂ 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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