Premium
The number of spanning trees in buckminsterfullerene
Author(s) -
Brown T. J. N.,
Mallion R. B.,
Pollak P.,
de Castro Branca R. M.,
Gomes J. A. N. F.
Publication year - 1991
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540120909
Subject(s) - buckminsterfullerene , spanning tree , combinatorics , mathematics , modulo , minimum spanning tree , cluster (spacecraft) , order (exchange) , tree (set theory) , carbon fibers , discrete mathematics , computer science , fullerene , algorithm , physics , quantum mechanics , composite number , finance , economics , programming language
Abstract 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.