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Croatica Chemica Acta, Vol. 92 No. 4, 2019.

Original scientific paper

https://doi.org/10.5562/cca3602

Convexity Deficit of Benzenoids

Nino Bašić orcid id orcid.org/0000-0002-6555-8668 ; FAMNIT, University of Primorska, Koper, Slovenia
Sarah J. Berkemer orcid id orcid.org/0000-0003-2028-7670 ; Bioinformatics Group, Department for Computer Science, and Interdisciplinary Center for Bioinformatics, Leipzig University, Germany
Jörg Fallmann orcid id orcid.org/0000-0002-4573-9939 ; Bioinformatics Group, Department for Computer Science, and Interdisciplinary Center for Bioinformatics, Leipzig University, Germany
Patrick W. Fowler ; Department of Chemistry, University of Sheffield, Sheffield S3 7HF, UK
Thomas Gatter orcid id orcid.org/0000-0001-5567-3016 ; Bioinformatics Group, Department for Computer Science, and Interdisciplinary Center for Bioinformatics, Leipzig University, Germany
Tomaž Pisanski ; FAMNIT, University of Primorska, Koper, Slovenia
Nancy Retzlaff orcid id orcid.org/0000-0002-9231-4220 ; Bioinformatics Group, Department for Computer Science, and Interdisciplinary Center for Bioinformatics, Leipzig University, Germany
Peter F. Stadler orcid id orcid.org/0000-0002-5016-5191 ; Bioinformatics Group, Department for Computer Science, and Interdisciplinary Center for Bioinformatics, Leipzig University, Germany
Sara Sabrina Zemljič orcid id orcid.org/0000-0003-4026-0854 ; FAMNIT, University of Primorska, Koper, Slovenia

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Abstract

In 2012, a family of benzenoids was introduced by Cruz, Gutman, and Rada, which they called convex benzenoids. In this paper we introduce the convexity deficit, a new topological index intended for benzenoids and, more generally, fusenes. This index measures by how much a given fusene departs from convexity. It is defined in terms of the boundary-edges code. In particular, convex benzenoids are exactly the benzenoids having convexity deficit equal to 0. Quasi-convex benzenoids form the family of non-convex benzenoids that are closest to convex, i.e., they have convexity deficit equal to 1. Finally, we investigate convexity deficit of several important families of benzenoids.

This work is licensed under a Creative Commons Attribution 4.0 International License.

Keywords

Benzenoid; fusene; convexity deficit; convex benzenoid; quasi-convex benzenoid; pseudo-convex benzenoid

Hrčak ID:

237954

URI

https://hrcak.srce.hr/237954

Publication date:

18.11.2019.

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