Binomial-combinatorial properties of Clar structures (Q1096641)

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 what may be termed a `delayed' Fibonacci sequence, in contrast to their Kekulé counts which form a Fibonacci sequence. Several combinatorial properties of Clar counts are given (equations (3)- (30)). The results emphasize the advantage of using Clar structures as based on the valence-bond Hamiltonian instead of Kekulé structures.