“…We identify five families of Kekuléan structures: parallelograms M(m 1 + m 2 − µ, n 1 = n 2 ) and M(m 1 = m 2 , n 1 + n 2 − ν) with ZZ polynomials given by Equation (2), generalized ribbons Rb with ZZ polynomials given by Equation (4), horizontally overlapping parallelograms MhM(m 1 , n 1 , m 2 , n 2 , µ, ν) with ZZ polynomials given by Equation (30), intersecting parallelograms MxM(m 2 , n 2 , m 1 , n 1 , µ, ν) with ZZ polynomials given by Equation (35), and vertically overlapping parallelograms MvM(m 2 , n 2 , m 1 , n 1 , µ, ν) with ZZ polynomials given by Equation (20). All formulas are given in the form of multiple sums over binomial coefficients, bearing a close structural similarity to the ZZ polynomial of a pristine parallelogram M(m, n) given by Equation (2). In case of the subset of the composite benzenoids consisting of parallelograms M, generalized ribbons Rb, and vertically overlapping parallelograms MvM, we demonstrate formally the correctness of the derived formulas.…”