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Licensed Unlicensed Requires Authentication Published by De Gruyter September 13, 2006

Characterizing finite locally s-arc transitive graphs with a star normal quotient

  • Michael Giudici EMAIL logo , Cai Heng Li and Cheryl E Praeger
From the journal Journal of Group Theory


Let Γ be a finite locally (G, s)-arc transitive graph with s ≥ 2 such that G is intransitive on vertices. Then Γ is bipartite and the two parts of the bipartition are G-orbits. In previous work the authors showed that if G has a non-trivial normal subgroup intransitive on both of the vertex orbits of G, then Γ is a cover of a smaller locally s-arc transitive graph. Thus the ‘basic’ graphs to study are those for which G acts quasiprimitively on at least one of the two orbits. In this paper we investigate the case where G is quasiprimitive on only one of the two G-orbits. Such graphs have a normal quotient which is a star. We construct several infinite families of locally 3-arc transitive graphs and prove characterization results for several of the possible quasiprimitive types for G.

(Communicated by A. A. Ivanov)

Received: 2005-09-22
Revised: 2005-11-14
Published Online: 2006-09-13
Published in Print: 2006-09-01

© Walter de Gruyter

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