Abstract
The benzenoid classes of multiple zigzag chains, A (n, m ), and incomplete multiple zigzag chains. A (n, m, l), are considered. Numerical numbers of Kekulé structures (K ) are given for n up to 5 and m up to 10. A recurrence relation is developed for the K numbers of A(n, m) with fixed values of n; a general formulation for arbitrary m values was achieved. Six new benzenoid classes are studied in connection with the application of the John-Sachs theorem to double zigzag chains. A new approach to the K enumeration is introduced by nonlinearly dependent recurrence relations. Finally a new type of combinatorial K formulas in terms of determinants and based on the John-Sachs theorem , is introduced. The new enumeration techniques are applied to multiple zigzag chains.
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