## Analysing finite locally $s$-arc transitive graphs

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- by Michael Giudici, Cai Heng Li and Cheryl E. Praeger PDF
- Trans. Amer. Math. Soc.
**356**(2004), 291-317 Request permission

## Abstract:

We present a new approach to analysing finite graphs which admit a vertex intransitive group of automorphisms $G$ and are either locally $(G,s)$–arc transitive for $s \geq 2$ or $G$–locally primitive. Such graphs are bipartite with the two parts of the bipartition being the orbits of $G$. Given a normal subgroup $N$ which is intransitive on both parts of the bipartition, we show that taking quotients with respect to the orbits of $N$ preserves both local primitivity and local $s$–arc transitivity and leads us to study graphs where $G$ acts faithfully on both orbits and quasiprimitively on at least one. We determine the possible quasiprimitive types for $G$ 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.## References

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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
- MR Author ID: 655176
- ORCID: 0000-0001-5412-4656
- 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
- MR Author ID: 305568
- 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
- MR Author ID: 141715
- ORCID: 0000-0002-0881-7336
- Email: praeger@maths.uwa.edu.au
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2020034