%0 Journal Article
%T On the number of spanning trees in random regular graphs
%A Catherine Greenhill
%A Matthew Kwan
%A David Wind
%J Mathematics
%D 2013
%I arXiv
%X Let $d \geq 3$ be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random $d$-regular graph with $n$ vertices. (The asymptotics are as $n\to\infty$, restricted to even $n$ if $d$ is odd.) We also obtain the asymptotic distribution of the number of spanning trees in a uniformly random cubic graph, and conjecture that the corresponding result holds for arbitrary (fixed) $d$. Numerical evidence is presented which supports our conjecture.
%U http://arxiv.org/abs/1309.6710v2