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arXiv:1210.5704 [math.CO]AbstractReferencesReviewsResources

Counting graphs with different numbers of spanning trees through the counting of prime partitions

Jernej Azarija

Published 2012-10-21, updated 2012-10-23Version 2

Let A_n (n >= 1) be the set of all integers x such that there exists a connected graph on n vertices with precisely x spanning trees. In this paper, we show that |A_n| grows faster than sqrt{n}exp(2Pi*sqrt{n/log{n}/Sqrt(3)} This settles a question of Sedlacek.

Comments: 5 pages
Categories: math.CO
Subjects: 05A16
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