A formula for the number of spanning trees in circulant graphs with non-fixed generators and discrete tori
Abstract
We consider the number of spanning trees in circulant graphs of β n vertices with generators depending linearly on n. The matrix tree theorem gives a closed formula of β n factors, while we derive a formula of β-1 factors. Using the same trick, we also derive a formula for the number of spanning trees in discrete tori. Moreover, the spanning tree entropy of circulant graphs with fixed and non-fixed generators is compared.
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