The Cayley graphs of Zd and the limits of vertex-primitive graphs of HA -type

• Autores: K.V. Kostousov
• Localización: Siberian mathematical journal, ISSN 0037-4466, Vol. 48, Nº. 3, 2007, págs. 489-499
• Idioma: inglés
• DOI: 10.1007/s11202-007-0051-z
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups Zd. In this article we prove that for each d > 1 the set of Cayley graphs of Zd presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of Zd that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of Zd with crystallographic groups.