Sur les atomes d'un graphe de Cayley infini. (On the atoms of an infinite Cayley graph)
type: Item
instance of: scholarly article
title: Sur les atomes d'un graphe de Cayley infini. (On the atoms of an infinite Cayley graph)
zbMATH Open document ID: 0663.05057
DOI: 10.1016/0012-365X(89)90273-2
author: Yahya Ould Hamidoune
published in: Discrete Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let G be an infinite group and let S be a finite subset of G. The outconnectivity of the Cayley graph \(X=Cay(G,S)\) is \(\kappa^+(X)=Min\{| (FS)\setminus F|:\) F is a finite nonvoid subset of \(G\}\). A positive end is a finite subset R such that \(\kappa^+(X)=| (RS)\setminus R|\), which is minimal with respect to this property. We prove that there is a unique positive end containing 1. Moreover this end is a subgroup. As an application we deduce some properties of the connectivity which were known only in the finite case.
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 4083682
zbMATH Keywords: infinite group
zbMATH Keywords: Cayley graph
zbMATH Keywords: connectivity
MaRDI profile type: Publication
cites work: Q4121925
cites work: Quelques problèmes de connexite dans les graphes orientes
cites work: On the connectivity of Cayley digraphs
cites work: Sur la séparation dans les graphes de Cayley abéliens
cites work: On the connectivities of finite and infinite graphs
cites work: Eine Eigenschaft der Atome endlicher Graphen
cites work: Connectivity of transitive graphs
description: scientific article; zbMATH DE number 4083682