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Titolo: A class of finite symmetric graphs with 2arc transitive quotients
Autore: Li, CH; Praeger, CE; Zhou, SM;
 Indirizzi:
 Univ Western Australia, Dept Math & Stat, Perth, WA 6907, Australia Univ Western Australia Perth WA Australia 6907 Perth, WA 6907, Australia
 Titolo Testata:
 MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
,
volume: 129,
anno: 2000,
parte:, 1
pagine: 19  34
 SICI:
 03050041(200007)129:<19:ACOFSG>2.0.ZU;23
 Fonte:
 ISI
 Lingua:
 ENG
 Soggetto:
 PERMUTATIONGROUPS;
 Tipo documento:
 Article
 Natura:
 Periodico
 Settore Disciplinare:
 Physical, Chemical & Earth Sciences
 Citazioni:
 12
 Recensione:
 Indirizzi per estratti:
 Indirizzo: Li, CH Univ Western Australia, Dept Math & Stat, Perth, WA 6907, AustraliaUniv Western Australia Perth WA Australia 6907 WA 6907, Australia



 Citazione:
 C.H. Li et al., "A class of finite symmetric graphs with 2arc transitive quotients", MATH PROC C, 129, 2000, pp. 1934
Abstract
Let Gamma be a finite Gsymmetric graph whose vertex set admits a nontrivial Ginvariant partition B with block size v. A framework for studying such graphs Gamma was developed by Gardiner and Praeger which involved an analysis of the quotient graph Gamma(B) relative to B, the bipartite subgraph Gamma[B, C] of Gamma induced by adjacent blocks B, C of Gamma(B) and a certain 1design D(B) induced by a block B is an element of B. The present paperstudies the case where the size k of the blocks of D(B) satisfies k = v  1. In the general case, where k = v  1 greater than or equal to 2, the setwise stabilizer G(B) is doubly transitive on B and G is faithful on B. We prove that D(B) contains no repeated blocks if and only if Gamma(B) is (G, 2)arc transitive and give a method for constructing such a graph from a 2arc transitive graph with a selfpaired orbit on 3arcs. We show further that each such graph may be constructed by this method. In particular every 3arc transitive graph, and every Sarc transitive graph of even valency, mayoccur as Gamma(B) for some graph Gamma with these properties. We prove further that Gamma[B, C] congruent to Kv1,Kv1 if and only if Gamma(B) is (G, 3)arc transitive.
ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 02/06/20 alle ore 02:08:21