A Periodic Table for Polycyclic Aromatic Hydrocarbons. Part V. 1-Factorable, 2-Factorable, and Dewar Graph Structures Associated with Benzenoid Hydrocarbons

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Abstract
Further properties of a Formula Periodic Table for Benzenoid PAH6s are presented. Whether the number of components of 1-factor and 2-factor subgraphs of benzenoid hydrocarbons are even or odd and the sign of the aN coefficient of the characteristic polynomial is negative or positive are prescribed by this table. A method for computing the number of Dewar structures from the aac N-2 coefficient of the acrylic polynomial is reviewed. It is shown that a stronger correlation of resonance energy and In aac N-2 of In KNc exists than for In K where K = SC (structure count) aac N. It is conjectured that ethene is subspectral to all benzenoid PAH6 structures belonging to the Nc = 0(mod 4) row series of the formula periodic table for benzenoid PAH6s. Previous research from this laboratory has evolved a formula periodic table for PAH6s which for the first time unified formula/structure relationships of benzenoid hydrocarbons into a systematic framework [1]. Herein additional correlations of this periodic table are presented. Also, structural relationships of the coefficients of the acyclic and characteristic polynomials within the frame of this table are reviewed.

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