Separating rank 3 graphs

John Bamberg; Michael Giudici; Jesse Lansdown; Gordon F. Royle

doi:10.1016/j.ejc.2023.103732

Separating rank 3 graphs

John Bamberg, Michael Giudici, Jesse Lansdown, Gordon F. Royle

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We classify, up to some notoriously hard cases, the rank 3 graphs which fail to meet either the Delsarte or the Hoffman bound. As a consequence, we resolve the question of separation for the corresponding rank 3 primitive groups and give new examples of synchronising, but not QI, groups of affine type.

Original language	English
Article number	103732
Number of pages	13
Journal	European Journal of Combinatorics
Volume	112
DOIs	https://doi.org/10.1016/j.ejc.2023.103732
Publication status	Published - Aug 2023

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10.1016/j.ejc.2023.103732

https://arxiv.org/abs/2211.02326

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@article{946dee6f1bdc40368fc880ba50d2b7a5,

title = "Separating rank 3 graphs",

abstract = "We classify, up to some notoriously hard cases, the rank 3 graphs which fail to meet either the Delsarte or the Hoffman bound. As a consequence, we resolve the question of separation for the corresponding rank 3 primitive groups and give new examples of synchronising, but not QI, groups of affine type.",

author = "John Bamberg and Michael Giudici and Jesse Lansdown and Royle, {Gordon F.}",

note = "Funding Information: The authors acknowledge the support of the Australian Research Council Discovery Grant DP200101951 . Publisher Copyright: {\textcopyright} 2023 Elsevier Ltd",

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AU - Bamberg, John

AU - Giudici, Michael

AU - Lansdown, Jesse

AU - Royle, Gordon F.

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AB - We classify, up to some notoriously hard cases, the rank 3 graphs which fail to meet either the Delsarte or the Hoffman bound. As a consequence, we resolve the question of separation for the corresponding rank 3 primitive groups and give new examples of synchronising, but not QI, groups of affine type.

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DO - 10.1016/j.ejc.2023.103732

M3 - Article

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VL - 112

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

SN - 0195-6698

M1 - 103732

ER -

Separating rank 3 graphs

Abstract

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The synchronisation hierarchy of permutation groups

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Separating rank 3 graphs

Abstract

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The synchronisation hierarchy of permutation groups

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