Resistance Distances in Fullerene Graphs

Sa？etak Resistance distances are computed for all 1812 C60 fullerenes and found to correlate with the number of pentagon adjacencies and hence with relative energy. Within the set, the unique isolated-pen-tagon isomer has the lowest resistance distance (RT = 479482/209), the lowest Wiener index (W = 8340) and the highest Balaban index (J = 2025/2224). The most stable C40 fullerene isomer, one of two with the lowest achievable number of pentagon adjacencies, also has the lowest resistance distance in the set