Transactions of the American Mathematical Society

Author(s): Michael Giudici; Cai Heng Li; Cheryl E. Praeger
Journal: Trans. Amer. Math. Soc. 356 (2004), 291-317.
MSC (2000): Primary 05C25, 20B25
Posted: August 25, 2003
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Abstract: We present a new approach to analysing finite graphs which admit a vertex intransitive group of automorphisms

and are either locally

-arc transitive for $s \geq 2$ or

-locally primitive. Such graphs are bipartite with the two parts of the bipartition being the orbits of

. Given a normal subgroup

which is intransitive on both parts of the bipartition, we show that taking quotients with respect to the orbits of

preserves both local primitivity and local

-arc transitivity and leads us to study graphs where

acts faithfully on both orbits and quasiprimitively on at least one. We determine the possible quasiprimitive types for

in these two cases and give new constructions of examples for each possible type. The analysis raises several open problems which are discussed in the final section.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 05C25, 20B25

Michael Giudici
Affiliation: School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia
Email: giudici@maths.uwa.edu.au

Cai Heng Li
Affiliation: School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia
Email: li@maths.uwa.edu.au

Cheryl E. Praeger
Affiliation: School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia
Email: praeger@maths.uwa.edu.au

DOI: 10.1090/S0002-9947-03-03361-0
PII: S 0002-9947(03)03361-0
Received by editor(s): November 22, 2002
Posted: August 25, 2003
Additional Notes: This paper forms part of an Australian Research Council large grant project which supported the first author. The second author was supported by an ARC Fellowship
Copyright of article: Copyright 2003, American Mathematical Society

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