From Subkautz Digraphs to Cyclic Kautz Digraphs
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Kautz digraphs K(d, l) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz digraphs CK(d, l) were recently introduced by Böhmová, Huemer and the author, and some of its distance-related parameters were fixed. In this paper we propose a new approach to cyclic Kautz digraphs by introducing the family of subKautz digraphs sK(d, l), from where the cyclic Kautz digraphs can be obtained as line digraphs. This allows us to give exact formulas for the distance between any two vertices of both sK(d, l) and CK(d, l). Moreover, we compute the diameter and the semigirth of both families, also providing efficient routing algorithms to find the shortest path between any pair of vertices. Using these parameters, we also prove that sK(d, l) and CK(d, l) are maximally vertex-connected and super-edge-connected. Whereas K(d, `) are optimal with respect to the diameter, we show that sK(d, l) and CK(d, l) are optimal with respect to the mean distance, whose exact values are given for both families when l = 3. Finally, we provide a lower bound on the girth of CK(d, l and sK(d, l).
Is part ofJournal of Interconnection Networks, 2018, vol. 18, núm. 02n03, p. 1850006
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Böhmová, Katerina; Dalfó, Cristina; Huemer, Clemens (Faculty of Sciences and Mathematics, University of Nis, Serbia, 2017)We present a new kind of digraphs, called cyclic Kautz digraphs CK(d, ɭ), which are subdigraphs of the well-known Kautz digraphs K(d,ɭ). The latter have the smallest diameter among all digraphs with their number of ...
Dalfó, Cristina (Elsevier, 2017)Kautz digraphs K(d, `) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz CK(d, `) and the subKautz sK(d, 2) digraphs were ...
Comellas, Francesc; Dalfó, Cristina; Fiol, Miguel Angel (Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia, 2013)We study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can be used to built other ...