## 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
Full Text:

### References:

 [1] Baron, Fibonacci Q 23 pp 258– (1985) [2] Boesch, Graphs Combin 2 pp 191– (1986) · Zbl 0651.05028 [3] Boesch, SIAM J Alg Discr Methods 7 pp 89– (1986) · Zbl 0578.05046 [4] and Spectra of graphs, VEB Deutscher Verlag der Wissenschafen, Berlin, 1982. [5] Lonc, Networks 30 pp 47– (1997) · Zbl 0882.05073 [6] McKay, Eur J Combin 4 pp 149– (1983) · Zbl 0517.05043 [7] and Designing of regular graphs with the use of evolutionary computation, Proc Congress on Evolutionary Computation, Washington, DC, 1999, pp. 1550-1556. [8] Sedla?ek, Casop Pest Mat 91 pp 221– (1966) [9] Sedla?ek, Casop Pest Mat 94 pp 217– (1969) [10] Wojciechowski, J Franklin Inst 326 pp 889– (1989) · Zbl 0723.05071
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.