Analysing finite locally -arc transitive graphs

Authors:
Michael Giudici, Cai Heng Li and Cheryl E. Praeger

Journal:
Trans. Amer. Math. Soc. **356** (2004), 291-317

MSC (2000):
Primary 05C25, 20B25

DOI:
https://doi.org/10.1090/S0002-9947-03-03361-0

Published electronically:
August 25, 2003

MathSciNet review:
2020034

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Abstract | References | Similar Articles | Additional Information

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 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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Additional Information

**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:
https://doi.org/10.1090/S0002-9947-03-03361-0

Received by editor(s):
November 22, 2002

Published electronically:
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

Article copyright:
© Copyright 2003
American Mathematical Society