𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Sur les atomes d'un graphe de Cayley infini

✍ Scribed by Yahya Ould Hamidoune

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
351 KB
Volume
73
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

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 K+(X)=M~~{((FS~\F(:F

is a finite nonvoid subset of G). A positive end is a finite subset R such that K+(X) = ((RS)\ RI, 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.

📜 SIMILAR VOLUMES

Sur les quasi-noyaux d'un graphe
Sur les quasi-noyaux d'un graphe
✍ Pierre Duchet; Yahya Ould Hamidoune; Henry Meyniel 📂 Article 📅 1987 🏛 Elsevier Science 🌐 English ⚖ 237 KB

We define three classes of quasi-kernels for a directed graph. As a consequence, we show the existence of quasi-kernels in every progressively finite graph and in every locally finite graph, generalizing the result of Chv~ital and Lov~tsz which deals with the finite case. Our method shows that the p