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For a two-dimensional lattice $\Lambda$ with $n$ vertices, the number ofspanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ inthe thermodynamic limit. We present exact integral expression and numericalvalue for the asymptotic growth constant $z_\Lambda$ for spanning trees onvarious two-dimensional lattices with more than one type of vertex given in\cite{Okeeffe}. An exact closed-form expression for the asymptotic growthconstant is derived for net 14, and the asymptotic growth constants of net 27and the triangle lattice have the simple relation $z_{27} = (z_{tri}+\ln 4)/4$.Some integral identities are also obtained.

Spanning Trees on the Two-Dimensional Lattices with More Than One Type of Vertex