| J.-C. Bermond and F. O. Ergincan. Directed line hypergraphs. in preparation. |
....different definitions as mentioned above, and Kautz hypergraphs can be defined using the last two definitions. Details of these definitions can be found in [10] here we will only mention some techniques used in the generalization. To generalize the second definition, a new notion was introduced [14]: The directed line hypergraph, L(H) of a directed hypergraph H has the following vertex set and hyperarc set: V(L(H) E2E(H) f(uEv) j u 2 E Gamma ; v 2 E g E(L(H) v2V(H) f(EvF ) j E 3 v; F Gamma 3 vg; The in set and the out set of a hyperarc (EvF ) are, ....
J.-C. Bermond and F. O. Ergincan. Directed line hypergraphs. in preparation.
....and with logarithmic diameter, by ignoring the orientation of the buses of the generalized de Bruijn or Kautz bus networks. The connectivity, network load, and routing issues for both directed and undirected de Bruijn and Kautz bus networks are being considered in [4] and ongoing research. In [5], we show that definitions of the de Bruijn digraphs and of the Kautz digraphs using line digraph iterations can also be extended to hypergraphs by using the directed line hypergraph technique. Acknowledgements Fahir O. Ergincan would like to thank Dr. Johny Bond and Dr. Patrick Sol e for ....
J.-C. Bermond and F. O. Ergincan. Directed line hypergraphs. in preparation. 19
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