Constructing 2-Arc-Transitive Covers of Hypercubes

Michael Giudici, Caiheng Li, Yian Xu

Research output: Contribution to journal › Article

Abstract

We introduce the notion of a symmetric basis of a vector space equipped with a quadratic form, and provide a sufficient and necessary condition for the existence to such a basis. Symmetric bases are then used to study Cayley graphs of certain extraspecial 2-groups of order 2 2r+1 (r≥ 1), which are further shown to be normal Cayley graphs and 2-arc-transitive covers of 2r-dimensional hypercubes.

Original languageEnglish
JournalGraphs and Combinatorics
DOIs
Publication statusE-pub ahead of print - 7 Jun 2019

Fingerprint

Cayley Graph
Vector spaces
Hypercube
Arc of a curve
Cover
Quadratic form
Vector space
Necessary Conditions
Sufficient Conditions

Cite this

Giudici, Michael ; Li, Caiheng ; Xu, Yian. / Constructing 2-Arc-Transitive Covers of Hypercubes. In: Graphs and Combinatorics. 2019.
@article{73f8808c24a34c85b73e8b103bf4120f,
title = "Constructing 2-Arc-Transitive Covers of Hypercubes",
abstract = "We introduce the notion of a symmetric basis of a vector space equipped with a quadratic form, and provide a sufficient and necessary condition for the existence to such a basis. Symmetric bases are then used to study Cayley graphs of certain extraspecial 2-groups of order 2 2r+1 (r≥ 1), which are further shown to be normal Cayley graphs and 2-arc-transitive covers of 2r-dimensional hypercubes.",
keywords = "Extraspecial 2-group, Locally-primitive graph, Normal Cayley graph, Quadratic form, Symmetric basis",
author = "Michael Giudici and Caiheng Li and Yian Xu",
year = "2019",
month = "6",
day = "7",
doi = "10.1007/s00373-019-02049-8",
language = "English",
journal = "Graphs and Combinatorics",
issn = "0911-0119",
publisher = "Springer",

}

Giudici, M, Li, C & Xu, Y 2019, 'Constructing 2-Arc-Transitive Covers of Hypercubes' Graphs and Combinatorics. https://doi.org/10.1007/s00373-019-02049-8

Constructing 2-Arc-Transitive Covers of Hypercubes. / Giudici, Michael; Li, Caiheng; Xu, Yian.

In: Graphs and Combinatorics, 07.06.2019.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Constructing 2-Arc-Transitive Covers of Hypercubes

AU - Giudici, Michael

AU - Li, Caiheng

AU - Xu, Yian

PY - 2019/6/7

Y1 - 2019/6/7

N2 - We introduce the notion of a symmetric basis of a vector space equipped with a quadratic form, and provide a sufficient and necessary condition for the existence to such a basis. Symmetric bases are then used to study Cayley graphs of certain extraspecial 2-groups of order 2 2r+1 (r≥ 1), which are further shown to be normal Cayley graphs and 2-arc-transitive covers of 2r-dimensional hypercubes.

AB - We introduce the notion of a symmetric basis of a vector space equipped with a quadratic form, and provide a sufficient and necessary condition for the existence to such a basis. Symmetric bases are then used to study Cayley graphs of certain extraspecial 2-groups of order 2 2r+1 (r≥ 1), which are further shown to be normal Cayley graphs and 2-arc-transitive covers of 2r-dimensional hypercubes.

KW - Extraspecial 2-group

KW - Locally-primitive graph

KW - Normal Cayley graph

KW - Quadratic form

KW - Symmetric basis

UR - http://www.scopus.com/inward/record.url?scp=85067018286&partnerID=8YFLogxK

U2 - 10.1007/s00373-019-02049-8

DO - 10.1007/s00373-019-02049-8

M3 - Article

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

ER -

Giudici M, Li C, Xu Y. Constructing 2-Arc-Transitive Covers of Hypercubes. Graphs and Combinatorics. 2019 Jun 7. https://doi.org/10.1007/s00373-019-02049-8

Access to Document