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The number of spanning trees in buckminsterfullerene

✍ Scribed by T. J. N. Brown; R. B. Mallion; P. Pollak; Branca R. M. de Castro; J. A. N. F. Gomes

Publisher: John Wiley and Sons
Year: 1991
Tongue: English
Weight: 662 KB
Volume: 12
Category: Article
ISSN: 0192-8651
DOI: 10.1002/jcc.540120909

No coin nor oath required. For personal study only.

✦ Synopsis

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.

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