Catalogo Articoli (Spogli Riviste)

OPAC HELP

Titolo:
A class of finite symmetric graphs with 2-arc 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:
0305-0041(200007)129:<19:ACOFSG>2.0.ZU;2-3
Fonte:
ISI
Lingua:
ENG
Soggetto:
PERMUTATION-GROUPS;
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 2-arc transitive quotients", MATH PROC C, 129, 2000, pp. 19-34

Abstract

Let Gamma be a finite G-symmetric graph whose vertex set admits a non-trivial G-invariant 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 1-design 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 2-arc transitive graph with a self-paired orbit on 3-arcs. We show further that each such graph may be constructed by this method. In particular every 3-arc transitive graph, and every S-arc 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 K-v-1,K-v-1 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 28/03/20 alle ore 14:10:30