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Título:
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A geometric approach to dense Cayley digraphs of finite Abelian groups
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Autor/a:
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Aguiló Gost, Francisco de Asis L.; Fiol Mora, Miquel Àngel; Pérez Mansilla, Sonia
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Otros autores:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
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Abstract:
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We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related {\em minimum distance diagrams}. A {\em dilating} technique for these diagrams, which can be used for any degree of the digraph, is applied to generate the digraphs of the family. Moreover, two infinite families of digraphs with distinguished metric properties will be given using these methods. The first family contains digraphs with asymptotically large ratio between the order and the diameter as the degree increases (moreover it is the first known asymptotically dense family). The second family, for fixed degree $d=3$, contains digraphs with the current best known density. |
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Abstract:
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Peer Reviewed |
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Materia(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
-Geometry, Algebraic
-Cayley digraph
-minimum distance diagram
-dilation
-diameter
-density.
-Geometria algèbrica
-Classificació AMS::14 Algebraic geometry::14L Algebraic groups |
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Derechos:
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Tipo de documento:
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Artículo - Versión presentada
Objeto de conferencia |
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Editor:
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Elsevier
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Compartir:
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