The number of spanning trees in buckminsterfullerene

The theorem of Gutman et al. (1983) is applied to calculate the number of spanning trees in the carbon‐carbon connectivity‐network of the recently diagnosed C 60 ‐cluster buckminsterfullerene. This “complexity” turns out to be approximately 3.75 × 10 20 and it is found necessary to invoke the device of modulo arithmetic and the “Chinese Remainder Theorem” in order to evaluate it precisely on a small computer. The exact spanningtree count for buckminsterfullerene is 375 291 866 372 898 816 000, or, 2 25 × 3 4 × 5 3 × 11 5 × 19 3 . A “ringcurrent” calculation by the method of McWeeny may be based on any desired one of this vast number of spanning trees.