dc.contributor.author Balbuena Martínez, Maria Camino Teófila dc.contributor.author García-Vázquez, Pedro dc.date.accessioned 2011-05-05T10:08:57Z dc.date.available 2011-05-05T10:08:57Z dc.date.issued 2011 dc.identifier.citation Balbuena Martínez, Maria Camino Teófila; García-Vázquez, Pedro. On the connectivity and restricted edge-connectivity of 3-arc graphs. A: International Workshop on Optimal Networks Topologies. "Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010". Barcelona: Iniciativa Digital Politècnica, 2011, p. 79-89. dc.identifier.isbn 978-84-7653-565-3 dc.identifier.uri http://hdl.handle.net/2099/10351 dc.description.abstract A 3−arc of a graph G is a 4-tuple (y, a, b, x) of vertices such that both (y, a, b) and (a, b, x) are paths of length two in G. Let ←→G denote the symmetric digraph of a graph G. The 3-arc graph X(G) of a given graph G is defined to have vertices the arcs of ←→G. Two vertices (ay), (bx) are adjacent in X(G) if and only if (y, a, b, x) is a 3-arc of G. The purpose of this work is to study the edge-connectivity and restricted edge-connectivity of 3-arc graphs.We prove that the 3-arc graph X(G) of every connected graph G of minimum degree δ(G) ≥ 3 has edge-connectivity λ(X(G)) ≥ (δ(G) − 1)2; and restricted edge- connectivity λ(2)(X(G)) ≥ 2(δ(G) − 1)2 − 2 if κ(G) ≥ 2. We also provide examples showing that all these bounds are sharp. dc.format.extent 11 p. dc.language.iso eng dc.publisher Iniciativa Digital Politècnica dc.relation.ispartof International Workshop on Optimal Networks Topologies dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs dc.subject.lcsh Graph theory dc.subject.lcsh Discrete geometry dc.title On the connectivity and restricted edge-connectivity of 3-arc graphs dc.type Conference report dc.subject.lemac Grafs, Teoria de dc.subject.lemac Geometria discreta dc.description.peerreviewed Peer Reviewed dc.subject.ams Classificació AMS::05 Combinatorics::05C Graph theory dc.rights.access Open Access upcommons.citation.author Balbuena Martínez, Maria Camino Teófila; García-Vázquez, Pedro upcommons.citation.contributor International Workshop on Optimal Networks Topologies upcommons.citation.pubplace Barcelona upcommons.citation.published true upcommons.citation.publicationName Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010 upcommons.citation.startingPage 79 upcommons.citation.endingPage 89
﻿

### This item appears in the following Collection(s)

• 3er. 2010 [27]
Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, Barcelona, 9-11 June 2010
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder