格子图与环纹面的支撑树数的渐近定理

Asymptotic Enumeration Theorem for the Number of Spanning Trees in Grids and Tori

本文的主要结果如下：设Ｈ≥１，ｍｉｎ｛ｎ１，ｎ２，…，ｎｈ＋１｝＝ｍ≥３，ｐ＝ｎｉ，Ｈ１＝Ｐｎ１×…×Ｐｎｈ＋１是个格子图， Ｈ２＝ Ｃｎ１×…× Ｃｎｈ＋１是个环纹面， ｔ（Ｈ）表示 Ｈ的支撑树数，则。

Suppose that h ≥1, min{n1,n2,…,nh+1}=m≥3 H1= Pn1, ×… × Pnh+1 is a grid and H2 = Cn1, ×…×Cnh+1, is a torus. Let t(H) denote the number of spanning trees in a graph H. In this paper. it is proved that