Cardinalities of poly(p-phenylene) graphs

Recurrence relation for the cardinalities of linear and cylindrical poly(p-phenylene) (PPP) compounds has been developed that requires the cardinalities of two of their immediate lower homologues. Such recurrence relation reduces into analytical expressions for the cardinalities under transfer matrix formalism. Ambient condition density and bulk modulus of linear PPPs are found to bear excellent linear correlation with the inverse of logarithm of their cardinalities. Topological bond orders obtained from the cardinalities of such PPPs have been found to have good linear correlations with the respective Hückel bond orders.