Coverings, heat kernels and spanning trees

Fan Chung Shing-Tung Yau

Combinatorics mathscidoc:1912.43510

Journal of Combinatorics, 6, 163-184
We consider a graph G and a covering G 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 knlog k
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  title={Coverings, heat kernels and spanning trees},
  author={Fan Chung, and Shing-Tung Yau},
  booktitle={Journal of Combinatorics},
Fan Chung, and Shing-Tung Yau. Coverings, heat kernels and spanning trees. Vol. 6. In Journal of Combinatorics. pp.163-184.
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