Normal and non-normal cayley graphs

Yian Xu

Research output: ThesisDoctoral 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(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.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • The University of Western Australia
Thesis sponsors
Award date31 Dec 2018
DOIs
Publication statusUnpublished - 2018

Fingerprint

Cayley Graph
Graph in graph theory
Arc-transitive Graph
Strong Product
Cartesian product
Less than or equal to
Direct Product
Simple group
Divisible
Hypercube
Arc of a curve
Finite Group
Classify
Subgroup
Cover

Cite this

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title = "Normal and non-normal cayley graphs",
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.",
keywords = "normal Cayley graphs, NNN-graphs, NNN-property, regular groups, holomorph, 2-arc-transitive cover, extraspecial 2-groups",
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doi = "10.26182/5c496c0ddd2da",
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school = "The University of Western Australia",

}

Xu, Y 2018, 'Normal and non-normal cayley graphs', Doctor of Philosophy, The University of Western Australia. https://doi.org/10.26182/5c496c0ddd2da

Normal and non-normal cayley graphs. / Xu, Yian.

2018.

Research output: ThesisDoctoral Thesis

TY - THES

T1 - Normal and non-normal cayley graphs

AU - Xu, Yian

PY - 2018

Y1 - 2018

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

U2 - 10.26182/5c496c0ddd2da

DO - 10.26182/5c496c0ddd2da

M3 - Doctoral Thesis

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