De Bruijn and Kautz bus networks

Eulerian and Hamiltonian Dicycles in Directed Hypergraphs

“…By inversing the labeling of the hyperarcs, it has been proposed in [12] an equivalent definition for Kautz dihypergraphs: 12]). Let (d, n, s, m) be four positive integers, such that dn ≡ 0 (mod m) and sm ≡ 0 (mod n).…”

“…As example, we prove that if H is a weakly-connected, d-regular, s-uniform dihypergraph, then, for every k ≥ 1, L k (H) is Eulerian and Hamiltonian. In the second part, we study the Eulerian and Hamiltonian properties of special families of regular uniform dihypergraphs, the generalized de Bruijn and Kautz dihypergraphs [12].…”

“…In particular, de Bruijn and Kautz dihypergraphs and their generalizations, that were introduced in [12], have several properties that are beneficial in the design of large, dense, robust networks. They have been proposed as the underlying physical topologies for optical networks, as well as dense logical topologies for Logically Routed Networks (LRN) because of ease of routing, load balancing and congestion reduction, that are properties inherent in de Bruijn and Kautz networks.…”

Line Directed Hypergraphs

“…Note that condition (1) is needed in order to insure that i and i + n have the same out-neighborhood. Indeed, In [1] it is shown that…”

“…In [1] it is shown that the diameter of GB 2 (d, n, s, m) is ⌈log ds n⌉. In particular, when n = (ds) D and m = d 2 (ds) D−1 , the diameter is exactly D and these dihypergraphs are the standard de Bruijn dihypergraphs.…”