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We consider the number of spanning trees in circulant graphs of $\beta n$vertices with generators depending linearly on $n$. The matrix tree theoremgives a closed formula of $\beta n$ factors, while we derive a formula of$\beta-1$ factors. Using the same trick, we also derive a formula for thenumber of spanning trees in discrete tori. Moreover, the spanning tree entropyof circulant graphs with fixed and non-fixed generators is compared.

A formula for the number of spanning trees in circulant graphs with non-fixed generators and discrete tori