dc.contributor.author Böhmová, Katerina dc.contributor.author Dalfó Simó, Cristina dc.contributor.author Huemer, Clemens dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2015-12-17T10:58:24Z dc.date.available 2015-12-17T10:58:24Z dc.date.issued 2015 dc.identifier.citation Böhmová, K., Dalfo, C., Huemer, C. "On cyclic Kautz digraphs". 2015. dc.identifier.uri http://hdl.handle.net/2117/80848 dc.description.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 MCK(d, `) and it is derived from the Kautz digraphs K(d, `). It is well-known that the Kautz digraphs K(d, `) have the smallest diameter among all digraphs with their number of vertices and degree. We define the cyclic Kautz digraphs CK(d, `), whose vertices are labeled by all possible sequences a1 . . . a` of length `, 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 6= a`. The cyclic Kautz digraphs CK(d, `) have arcs between vertices a1a2 . . . a` and a2 . . . a`a`+1, with a1 6= a` and a2 6= a`+1. Unlike in Kautz digraphs K(d, `), any label of a vertex of CK(d, `) can be cyclically shifted to form again a label of a vertex of CK(d, `). We give the main parameters of CK(d, `): number of vertices, number of arcs, and diameter. Moreover, we construct the modified cyclic Kautz digraphs MCK(d, `) to obtain the same diameter as in the Kautz digraphs, and we show that MCK(d, `) are d-out-regular. Finally, we compute the number of vertices of the iterated line digraphs of CK(d, `). dc.format.extent 20 p. dc.language.iso eng dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta dc.subject.lcsh Graph theory dc.title On cyclic Kautz digraphs dc.type External research report dc.subject.lemac Grafs, Teoria de dc.contributor.group Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions dc.contributor.group Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta dc.rights.access Open Access drac.iddocument 17270086 dc.description.version Preprint upcommons.citation.author Böhmová, K.; Dalfo, C.; Huemer, C. upcommons.citation.published true
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