Circumscribing certain polygonal systems
type: Item
instance of: scholarly article
title: Circumscribing certain polygonal systems
zbMATH Open document ID: 0849.52002
DOI: 10.1016/0166-218X(95)00011-F
author: Sven J. Cyvin
author: B. N. Cyvin
author: J. Brunvoll
author: E. Keith Lloyd
published in: Discrete Applied Mathematics
publication date: 1996-11-05T00:00:00Z
review text: A polygonal system \(P_q\) is a planar graph which consists of \(q\)-gons. Such a system corresponds to a polycyclic conjugated hydrocarbon with chemical formula \(C_nH_s\). A system \(P_q\) may be enlarged by circumscribing repeatedly bands of \(q\)-gons. For these enlarged systems some invariants (e.g. the number of internal vertices) are determined. The results for \(q = 6\) (corresponding to benzenoid hydrocarbons) and \(q > 6\) are different. For a single \(q\)-gon and its circumscribed systems the invariants may be expressed by Fibonacci numbers. This is a special case of Harborth's mosaic graphs.
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 897418
zbMATH Keywords: polygonal systems
zbMATH Keywords: Fibonacci numbers
zbMATH Keywords: mosaic graphs
reviewed by: Erhard Heil
MaRDI profile type: Publication
cites work: Q5753988
cites work: Q4800067
cites work: Q4186365
cites work: On the cell-growth problem for arbitrary polygons
cites work: The enumeration of tree-like polyhexes
cites work: Q5749312
cites work: Q5686068
cites work: On general dissections of a polygon
cites work: Q3971631
full work available at URL: 0166-218x(95)00011-f
OpenAlex ID: W2047481948
description: scientific article; zbMATH DE number 897418