Convexity deficit of benzenoids
Combinatorics
2020-05-19 v1
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.
Cite
@article{arxiv.2003.09716,
title = {Convexity deficit of benzenoids},
author = {Nino Bašić and Sarah Berkemer and Jörg Fallmann and Patrick W. Fowler and Thomas Gatter and Tomaž Pisanski and Nancy Retzlaff and Peter F. Stadler and Sara S. Zemljič},
journal= {arXiv preprint arXiv:2003.09716},
year = {2020}
}
Comments
17 pages, 8 figures, 3 tables