Counting graphs with different numbers of spanning trees through the counting of prime partitions
Combinatorics
2012-10-24 v2
Abstract
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.
Cite
@article{arxiv.1210.5704,
title = {Counting graphs with different numbers of spanning trees through the counting of prime partitions},
author = {Jernej Azarija},
journal= {arXiv preprint arXiv:1210.5704},
year = {2012}
}
Comments
5 pages