New structural parameters of fullerenes for principal component analysis

Abstract.

The Kekulé structure count and the permanent of the adjacency matrix of fullerenes are related to structural parameters involving the presence of contiguous pentagons p, q, r, q/p and r/p, where p is the number of edges common to two pentagons, q is the number of vertices common to three pentagons and r is the number of pairs of nonadjacent pentagons adjacent to another common pentagon. The cluster analysis of the structural parameters allows classification these parameters. Principal component analysis (PCA) of the structural parameters and the cluster analyses of the fullerenes permit their classification. PCA clearly distinguishes five classes of fullerenes. The cluster analysis of fullerenes is in agreement with PCA classification. Cluster analysis shows greatest similarity for the q−q/p and r–r/p pairs. PCA provides five orthogonal factors F ₁−F ₅. The use of F ₁ gives an error of 28%. The inclusion of F ₂ decreases the error to 2%.