BINOMIAL-COMBINATORIAL PROPERTIES OF CLAR STRUCTURES

A Clar structure is defined to be a maximal independent set of vertices of the Clar graph of the corresponding benzenoid hydrocarbon. A special type of coloring, called a Clar coloring which is a specific type of 2-coloring is applied to Clar structures of two types of benzenoid hydrocarbons, viz. , (a) nonbranched all-benzenoid systems, and (b) necklace-type hydrocarbons. It is found that the Clar counts of these two systems define whay may be termed a 'delayed' Fibonacci sequence, in contrast to their Kekule counts which form a Fibonacci sequence. Several combinatorial properties of Clar counts are given. The results emphasize the advantage of using Clar structures as bases of the valence-bond Hamiltonian instead of Kekule structures.