On Cyclic Kautz Digraphs
Katerina B\"ohmov\'a, Cristina Dalf\'o, Clemens Huemer

TL;DR
This paper introduces modified cyclic Kautz digraphs that achieve minimal diameter for given vertices and out-degree, extending Kautz digraph properties with new cyclic constraints and regularity features.
Contribution
It defines cyclic Kautz digraphs with cyclic label properties, derives their parameters, and constructs modified versions with minimal diameter and regularity.
Findings
Defined cyclic Kautz digraphs with new cyclic label conditions.
Calculated key parameters: vertices, arcs, diameter.
Constructed modified digraphs with minimal diameter and regularity.
Abstract
A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and out-degree there is no other digraph with a smaller diameter. This new family is called modified cyclic digraphs and it is derived from the Kautz digraphs . %It is not common to find non-regular digraphs with minimal diameter given their number of vertices and out-degree. It is well-known that the Kautz digraphs have the smallest diameter among all digraphs with their number of vertices and degree. We define the cyclic Kautz digraphs , whose vertices are labeled by all possible sequences of length , such that each character is chosen from an alphabet containing…
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Interconnection Networks and Systems
