Isomer number patterns in aromatic hydrocarbon chemistry: the numbers speak for themselves

The unique organizational framework for polycyclic aromatic hydrocarbons developed by us has led to the discovery of number patterns for their number of isomers. Constant-isomer series are generated by repetitive circumscribing of a given set of isomers. Benzenoid, fluoranthenoid, indacenoid, and primitive coronoid constant isomer series possess twin isomer numbers with members having corresponding topologies. The concepts of strictly pericondensed, strain-free, Clar’s aromatic sextet, and symmetry are interconnected in the topological correspondence between strictly pericondensed and total resonant sextet (TRS) benzenoid hydrocarbons. In a plot of TRS isomer numbers on the Formula Periodic Table for Total Resonant Sextet Benzenoids [Table PAH6(TRS)] which is a subset of Table PAH6 for ordinary benzenoids, structural correlations in isomer numbers, symmetry distributions, and empty rings between various strain-free TRS benzenoids are presented. These chemical graph theoretical results belong to the branch of mathematics called number theory.