Coverings, Heat Kernels and Spanning Trees
نویسندگان
چکیده
We consider a graph G and a covering G̃ of G and we study the relations of their eigenvalues and heat kernels. We evaluate the heat kernel for an infinite k-regular tree and we examine the heat kernels for general k-regular graphs. In particular, we show that a k-regular graph on n vertices has at most (1 + o(1)) 2 log n kn log k (k − 1)k−1 (k2 − 2k)k/2−1 n spanning trees, which is best possible within a constant factor.
منابع مشابه
Coverings, heat kernels and spanning trees
We consider a graph G and a covering G̃ of G and we study the relations of their eigenvalues and heat kernels. We evaluate the heat kernel for an infinite k-regular tree and we examine the heat kernels for general k-regular graphs. In particular, we show that a k-regular graph on n vertices has at most (1 + o(1)) 2 log n kn log k ( (k − 1)k−1 (k2 − 2k)k/2−1 )n spanning trees, which is best possi...
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 6 شماره
صفحات -
تاریخ انتشار 1999