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 C60-cluster buckminsterfullerene. This "complexity" turns out to be approximately 3.75 x 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 spanning-tree count for buckminsterfullerene is 375 291 866 372 898 816 000, or, 2(25) x 3(4) x 5(3) x 11(5) x 19(3). A "ring-current" calculation by the method of McWeeny may be based on any desired one of this vast number of spanning trees.