Normal and non-normal cayley graphs

Yian Xu

doi:10.26182/5c496c0ddd2da

Normal and non-normal cayley graphs

Yian Xu

School of Physics, Mathematics and Computing

Research output: Thesis › Doctoral Thesis

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Abstract

This thesis mainly studies NNN-graphs and NNN-properties for finite groups. We first show that applying Cartesian product, direct product and strong product respectively to an NNN-graph and finitely many normal Cayley graphs construct new NNN-graphs. Next we solve the NNN-property for simple groups, (Z₂)^d, and Zn where n is not divisible by 8. We classify the regular subgroups of Hoi(Z₂^k) and solve the NNN-property for Z₂^k with k less than or equal to 6. In this thesis, we also study 2-arc transltive covers of hypercubes and construct new 2-arc-transitive graphs which are normal Cayley graphs.

Original language	English
Qualification	Doctor of Philosophy
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Morgan, Luke, Supervisor Giudici, Michael, Supervisor Li, Cai-Heng, Supervisor
Thesis sponsors	Australian Government Research Training Program
Award date	31 Dec 2018
DOIs	https://doi.org/10.26182/5c496c0ddd2da
Publication status	Unpublished - 2018

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THESIS - DOCTOR OF PHILOSOPHY - XU Yian - 2018
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Cite this

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abstract = "This thesis mainly studies NNN-graphs and NNN-properties for finite groups. We first show that applying Cartesian product, direct product and strong product respectively to an NNN-graph and finitely many normal Cayley graphs construct new NNN-graphs. Next we solve the NNN-property for simple groups, (Z2)d, and Zn where n is not divisible by 8. We classify the regular subgroups of Hoi(Z2k) and solve the NNN-property for Z2k with k less than or equal to 6. In this thesis, we also study 2-arc transltive covers of hypercubes and construct new 2-arc-transitive graphs which are normal Cayley graphs.",

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N2 - This thesis mainly studies NNN-graphs and NNN-properties for finite groups. We first show that applying Cartesian product, direct product and strong product respectively to an NNN-graph and finitely many normal Cayley graphs construct new NNN-graphs. Next we solve the NNN-property for simple groups, (Z2)d, and Zn where n is not divisible by 8. We classify the regular subgroups of Hoi(Z2k) and solve the NNN-property for Z2k with k less than or equal to 6. In this thesis, we also study 2-arc transltive covers of hypercubes and construct new 2-arc-transitive graphs which are normal Cayley graphs.

AB - This thesis mainly studies NNN-graphs and NNN-properties for finite groups. We first show that applying Cartesian product, direct product and strong product respectively to an NNN-graph and finitely many normal Cayley graphs construct new NNN-graphs. Next we solve the NNN-property for simple groups, (Z2)d, and Zn where n is not divisible by 8. We classify the regular subgroups of Hoi(Z2k) and solve the NNN-property for Z2k with k less than or equal to 6. In this thesis, we also study 2-arc transltive covers of hypercubes and construct new 2-arc-transitive graphs which are normal Cayley graphs.

KW - normal Cayley graphs

KW - NNN-graphs

KW - NNN-property

KW - regular groups

KW - holomorph

KW - 2-arc-transitive cover

KW - extraspecial 2-groups

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DO - 10.26182/5c496c0ddd2da

M3 - Doctoral Thesis

ER -

Normal and non-normal cayley graphs

Abstract

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