Ehrenmüller, JuliaJuliaEhrenmüllerRué, JuanjoJuanjoRué2020-04-292020-04-292016-04-01Advances in Applied Mathematics (75): 18-55 (2016-04-01)http://hdl.handle.net/11420/5960By means of analytic techniques we show that the expected number of spanning trees in a connected labelled series-parallel graph on n vertices chosen uniformly at random satisfies an estimate of the forms sρ-n(1+o(1)), where s and ρ are computable constants, the values of which are approximately s ≈ 0.09063 and ρ-1 ≈ 2.08415. We obtain analogous results for subfamilies of series-parallel graphs including 2-connected series-parallel graphs, 2-trees, and series-parallel graphs with fixed excess.en0196-885820161855MSC primary 05A16secondary 05C10Journal Article10.1016/j.aam.2015.12.001Other