Constructing 2-Arc-Transitive Covers of Hypercubes

Michael Giudici; Caiheng Li; Yian Xu

doi:10.1007/s00373-019-02049-8

Constructing 2-Arc-Transitive Covers of Hypercubes

Michael Giudici, Caiheng Li, Yian Xu

Mathematics and Statistics

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 ²^r⁺¹ (r≥ 1), which are further shown to be normal Cayley graphs and 2-arc-transitive covers of 2r-dimensional hypercubes.

Original language	English
Journal	Graphs and Combinatorics
DOIs	https://doi.org/10.1007/s00373-019-02049-8
Publication status	E-pub ahead of print - 7 Jun 2019

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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 = jun,

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doi = "10.1007/s00373-019-02049-8",

language = "English",

journal = "Graphs and Combinatorics",

issn = "0911-0119",

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T1 - Constructing 2-Arc-Transitive Covers of Hypercubes

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AU - Li, Caiheng

AU - Xu, Yian

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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

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SN - 0911-0119

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