## Generalized de Bruijn digraphs.(English)Zbl 0654.05036

Consider the directed graphs with n labelled vertices and e edges. Let $$A_{n,e}$$ denote the number of these graphs that are acyclic and let $$C_{n,e}$$ denote the number that are weakly connected. Let $$a_{n,e}$$ and $$c_{n,e}$$ denote the corresponding numbers for unlabelled graphs. The authors show that $$A_{n,e}\sim C_{n,e}\sim n!a_{n,e}\sim n!C_{n,e}$$ when $$\epsilon <2e/n(n-1)<1-\epsilon.$$
Reviewer: J.W.Moon

### MSC:

 05C20 Directed graphs (digraphs), tournaments 05C30 Enumeration in graph theory

### Keywords:

de Bruijn graphs; connectivity; diameter; directed graphs
Full Text:

### References:

 [1] Du, IEEE Trans. Comput. C-34 pp 1025– (1985) [2] Esfahanian, IEEE Trans. Comput. C-34 pp 777– (1985) [3] Imase, IEEE Trans. Comput. C-30 pp 439– (1981) [4] Imase, IEEE Trans. Comput. C-32 pp 782– (1983) [5] Imase, IEEE Trans. Comput. C-34 pp 267– (1985) [6] Lawrie, P. IEEE Trans. Comput. C-24 (1975) [7] Fault-tolerant multiprocessor and VLSI-based systems communication architecture. In Fault Tolerant Computing Theory and Techniques, Vol. II (ed. ). Prentice-Hall, Englewood Cliffs, NJ (1986). [8] Pradhan, IEEE Trans. Comput. C-31 pp 863– (1982) [9] and , Direct graphs with minimum diameter and maximal connectivity. School of Engineering, Oakland University Tech. Rep., July 1980. [10] Stone, IEEE Trans. Comput. C-20 pp 153– (1971)
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.