# On the Saxl graph of a permutation group

@article{Burness2017OnTS,
title={On the Saxl graph of a permutation group},
author={Timothy C. Burness and Michael Giudici},
journal={Mathematical Proceedings of the Cambridge Philosophical Society},
year={2017},
volume={168},
pages={219 - 248}
}
• Published 11 December 2017
• Mathematics
• Mathematical Proceedings of the Cambridge Philosophical Society
Abstract Let G be a permutation group on a set Ω. A subset of Ω is a base for G if its pointwise stabiliser in G is trivial. In this paper we introduce and study an associated graph Σ(G), which we call the Saxl graph of G. The vertices of Σ(G) are the points of Ω, and two vertices are adjacent if they form a base for G. This graph encodes some interesting properties of the permutation group. We investigate the connectivity of Σ(G) for a finite transitive group G, as well as its diameter…

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