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Title:
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The diameter of cyclic Kautz digraphs
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Author:
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Böhmová, Katerina; Dalfó, Cristina; Huemer, Clemens
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Notes:
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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 vertices and degree.
Cyclic Kautz digraphs CK(d, ɭ) have vertices labeled by all possible sequences a1 . . . aɭ
of length ɭ, such that each character ai is chosen from an alphabet containing d + 1 distinct symbols, where the consecutive characters in the sequence are different (as in Kautz
digraphs), and now also requiring that a1 ≠ aɭ. Their arcs are between vertices a1a2 . . . aɭ and a2 . . . aɭ aɭ + 1, with a1 ≠ aɭ and a2 ≠ aɭ + 1.
We give the diameter of CK(d, ɭ) for all the values of d and ɭ, and also its number of
vertices and arcs.
Research of C. Dalfo is supported by projects MINECO MTM2014-60127-P, and AGAUR 2014SGR1147. Research of C. Huemer is supported by projects MINECO MTM2015-63791-R, and AGAUR 2014SGR46. C. Dalfo and C. Huemer have also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie SkłodowskaCurie grant agreement No 734922. |
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Subject(s):
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-Digraph
-Diameter
-Kautz digraph |
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Rights:
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cc-by-nc-nd (c) Böhmová, Katerina et al., 2017
http://creativecommons.org/licenses/by-nc-nd/4.0/deed.ca
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Document type:
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Article
acceptedVersion |
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Published by:
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Faculty of Sciences and Mathematics, University of Nis, Serbia
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