Coronoids, Patches and Generalised Altans

Abstract

In this paper we revisit coronoids, in particular multiple coronoids. We consider a mathematical formalisation of the theory of coronoid hydrocarbons that is solely based on incidence between hexagons of the infinite hexagonal grid in the plane. In parallel, we consider perforated patches, which generalise coronoids: in addition to hexagons, other polygons may also be present. Just as coronoids may be considered as benzenoids with holes, perforated patches are patches with holes. Both cases, coronoids and perforated patches, admit a generalisation of the altan operation that can be performed at several holes simultaneously. A formula for the number of Kekul\'e structures of a generalised altan can be derived easily if the number of Kekul\'e structures is known for the original graph. Pauling Bond Orders for generalised altans are also easy to derive from those of the original graph.