Constructing 2-Arc-Transitive Covers of Hypercubes

Research output: Contribution to journalArticle

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

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

Cite this

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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",

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

In: Graphs and Combinatorics, 07.06.2019.

Research output: Contribution to journalArticle

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AU - Li, Caiheng

AU - Xu, Yian

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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.

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KW - Extraspecial 2-group

KW - Locally-primitive graph

KW - Normal Cayley graph

KW - Quadratic form

KW - Symmetric basis

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DO - 10.1007/s00373-019-02049-8

M3 - Article

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

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