The Factorisation of Chemical Graphs and Their Polynomials: A Polynomial Diyision Approach

Recent advances in computational methods allow the Characteristic and Acyclic Polynomials of a Chemical Graph to be calculated easily. A consequence of this is that checking for a zero-value remainder after computer assisted polynomial division is sometimes the simplest way of testing suspected factors of a chemical graph. The technique is simple enough to apply on a routine basis when characteristic or acyclic polynomials need to be solved. Among appropriate choices for test are linear polyenes and rings, because their roots are already independently available in closed form and they do occur as factors in a significant number of structures. Examination of an arbitrary set of structures showed that the acyclic polynomials of non-cyclic structures tend to be the most easily factorisable, followed by characteristic polynomials of cyclic structures and (least easily factorisable) the acyclic polynomials of the same cyclic structures.