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

الأصل · EN

Let Aₙ (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 |Aₙ| grows faster than sqrtnexp(2Pi*sqrtn/logn/Sqrt(3) This settles a question of Sedlacek.