From Subkautz Digraphs to Cyclic Kautz Digraphs

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2018Suggested citation
Dalfó, Cristina;
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(2018)
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From Subkautz Digraphs to Cyclic Kautz Digraphs.
Journal of Interconnection Networks, 2018, vol. 18, núm. 02n03, p. 1850006.
https://doi.org/10.1142/S0219265918500068.
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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 of
Journal of Interconnection Networks, 2018, vol. 18, núm. 02n03, p. 1850006European research projects
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