Strongly Subspectral Series Containing the Cyclobutadiene Moiety

Series of strongly subspectral molecular graphs (having a preponderance of common eigenvalues) corresponding to conjugated hydrocarbon polyenes containing cyclobutadiene moieties are presented and their electronic/structural properties studied

Acyclic and Characteristic Polynomial of Regular Conjugated Polymers and Their Derivatives

A method to study the acyclic and characteristic polynomial of regular conjugated polymers is described. For a regular polymer with l bonds linking the monomer units, one first builds a 2\u27X21 polynomial matrix T1. Its matrix elements are acyclic polynomials of the monomer unit graph and its subgraphs obtained by successive deletion of atoms serving as the linking sites. The acyclic polynomials of the fasciagraph (representing an open polymeric chain) and some of its subgraphs are then obtained as the appropriate matrix elements of Ti" where M stands for the degree of polymerization of the polymer under consideration. For the rotagraph (representing the polymeric chain closed on itself) the acyclic polynomial equal the trace of T1". It is proved that the acyclic polynomials of regular polymers and some of their derivatives satisfy recursion formulae of the same form which contain 21 + 1 terms. The coefficients appearing in the recursion are derived only from the knowledge of the matrix Ti and are, therefore, independent of M. As far as the characteristic polynomial of a regular polymer is concerned, here we apply an analogon of the Ti-formalism only for the special case of l = 1 and reproduce an already known recursion formula. However, a new determinantal representation of the characteristic polynomial of a polymer as well as its explicit expression in terms of the characteristic polynomials of monomer graph and its subgraphs is established for this special case

Strongly Subspectral Series Containing the Cyclobutadiene Moiety

Series of strongly subspectral molecular graphs (having a preponderance of common eigenvalues) corresponding to conjugated hydrocarbon polyenes containing cyclobutadiene moieties are presented and their electronic/structural properties studied