Permanents of adjacency matrices of fullerenes

This study examines the relationships between structural parameters for 28 Fullerenes and the permanents of their adjacency matrices, per(A). In particular, the structural parameters examined were related to the adjoining of pentagons. A new parameter, r, was introduced which counts contiguous pentagon triplets that have no single vertex in common. The quantity well-correlated with structure was not per(A) itself, but ln(per(A))/lnK, where K is the Kekule structure count. For all 28 fullernes, ln(per(A))/lnK > 2, contrary to expectations.