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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The finite vertex-primitive and vertex-biprimitive $s$-transitive graphs for $s\ge 4$
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by Cai Heng Li PDF
Trans. Amer. Math. Soc. 353 (2001), 3511-3529 Request permission

Abstract:

A complete classification is given for finite vertex-primitive and vertex-biprimitive $s$-transitive graphs for $s\ge 4$. The classification involves the construction of new 4-transitive graphs, namely a graph of valency 14 admitting the Monster simple group $\text {M}$, and an infinite family of graphs of valency 5 admitting projective symplectic groups $\text {PSp}(4,p)$ with $p$ prime and $p\equiv \pm 1$ (mod 8). As a corollary of this classification, a conjecture of Biggs and Hoare (1983) is proved.
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Additional Information
  • Cai Heng Li
  • Affiliation: Department of Mathematics and Statistics, The University of Western Australia, Nedlands, WA 6907, Australia
  • MR Author ID: 305568
  • Email: li@maths.uwa.edu.au
  • Received by editor(s): November 12, 1999
  • Received by editor(s) in revised form: July 11, 2000
  • Published electronically: April 24, 2001
  • Additional Notes: This work forms a part of an ARC project and is supported by an ARC Fellowship
    The author is grateful to C.E. Praeger, A.A. Ivanov and R. Weiss for their helpful comments on the work, and to the referee for constructive suggestions
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 3511-3529
  • MSC (2000): Primary 05C25, 20B05
  • DOI: https://doi.org/10.1090/S0002-9947-01-02768-4
  • MathSciNet review: 1837245