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 › peer-review

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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10.1007/s00373-019-02049-8

https://arxiv.org/abs/1805.06371

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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.",

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AU - Li, Caiheng

AU - Xu, Yian

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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.

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KW - Locally-primitive graph

KW - Normal Cayley graph

KW - Quadratic form

KW - Symmetric basis

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JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

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Constructing 2-Arc-Transitive Covers of Hypercubes

Abstract

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