Hexagonal systems with the one-to-one correspondence between geometric and algebraic Kekulé structures

An algebraic Kekulé structure (AKS) of a hexagonal system H is a function obtained from a geometric Kekulé structure (GKS) such that assign each hexagon of H a number according to the following way: each double bond in GKS that belongs to only one hexagon contributes 2 to the function value of the hexagon and each double bond that is shared by two hexagons contributes 1 to each one of these two hexagons. We obtain the following two results: There exists a one-to-one correspondence between GKSs and AKSs of benzenoid parallelogram Bp,q, except B1,1 and B2,2; There exists a one-to-one correspondence between GKSs and AKSs of a hexagonal system with no B2,2 as its subgraph, except B1,1.