Resistance distances in fullerene graphs

Resistance distances are computed for all 1812 C 6 0 fullerenes and found to correlate with the number of pentagon adjacencies and hence with relative energy. Within the set, the unique isolated-pentagon isomer has the lowest resistance distance (R T = 479482/209), the lowest Wiener index (W = 8340) and the highest Balaban index (J = 2025/2224). The most stable C 4 0 fullerene isomer, one of two with the lowest achievable number of pentagon adjacencies, also has the lowest resistance distance in the set.