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arXiv · 2003.09716

Convexity deficit of benzenoids

Nino Bašić·Sarah Berkemer·Jörg Fallmann·Patrick W. Fowler·Thomas Gatter·Tomaž Pisanski·Nancy Retzlaff·Peter F. Stadler·Sara S. Zemljič
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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.

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Nino Bašić, Sarah Berkemer, Jörg Fallmann, Patrick W. Fowler, Thomas Gatter, Tomaž Pisanski, Nancy Retzlaff, Peter F. Stadler, Sara S. Zemljič. 2020-03-21. Convexity deficit of benzenoids. https://doi.org/10.5562/cca3602

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