Convexity deficit of benzenoids

Convexity deficit of benzenoids

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 c...

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Veröffentlicht in:arXiv.org 2020-03
Hauptverfasser: Bašić, Nino, Berkemer, Sarah, Fallmann, Jörg, Fowler, Patrick W, Gatter, Thomas, Pisanski, Tomaž, Retzlaff, Nancy, Stadler, Peter F, Zemljič, Sara S
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Benzenoids
Convexity
Mathematics - Combinatorics
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container_title arXiv.org
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creator Bašić, Nino
Berkemer, Sarah
Fallmann, Jörg
Fowler, Patrick W
Gatter, Thomas
Pisanski, Tomaž
Retzlaff, Nancy
Stadler, Peter F
Zemljič, Sara S
description 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.
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subjects Benzenoids
Convexity
Mathematics - Combinatorics
title Convexity deficit of benzenoids
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