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On the number of spanning trees in directed circulant graphs. (English) Zbl 0974.05043

Summary: Let \(g_k(n)\) [respectively, \(f_k(n)\)] be the maximum number of spanning trees in directed circulant graphs (respectively, regular directed graphs) with \(n\) vertices and out-degrees equal to \(k>1\). We show that \(g_k(n)= k^{n(1+ o(1))}\) and \(f_k(n)= k^{n(1+ o(1))}\). Moreover, we prove that \(g_2(n)= \lfloor (2^n+ 1)/3\rfloor\).

MSC:

05C30 Enumeration in graph theory
05C05 Trees
94C15 Applications of graph theory to circuits and networks
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References:

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