Spanning Trees on Lattices and Integration Identities

Abstract

For a lattice $\Lambda$ with $n$ vertices and dimension $d$ equal or higher than two, the number of spanning trees $N_{ST}(\Lambda )$ grows asymptotically as $\exp (n{z}_{\Lambda })$ in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant $z_{\Lambda }$ for spanning trees on several lattices. By taking different unit cells in the calculation, many integration identities can be obtained. We also give $z_{\Lambda (p)}$ on the homeomorphic expansion of $k$-regular lattices with $p$ vertices inserted on each edge.

15 pages, 3 figures, 1 table

References in corpus (1)

• Some Exact Results for Spanning Trees on Lattices

Cited by in corpus (2)

• Spanning trees on the Sierpinski gasket
• Asymptotic energy of graphs