Matching Polynomial-Based Similarity Matrices and Descriptors for Isomers of Fullerenes

I have computed the matching polynomials of a number of isomers of fullerenes of various sizes with the objective of developing molecular descriptors and similarity measures for isomers of fullerenes on the basis of their matching polynomials. Two novel matching polynomial-based topological descriptors are developed, and they are demonstrated to have the discriminating power to contrast a number of closely related isomers of fullerenes. The number of ways to place up to seven disjoint dimers on fullerene isomers are shown to be identical, as they are not structure-dependent. Moreover, similarity matrices that provide quantitative similarity measures among a given set of isomers of fullerenes are developed from their matching polynomials and are shown to provide robust quantitative measures of similarity.