Circumscribing certain polygonal systems (Q1917326)

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.