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 language | English |
---|---|
Journal | Graphs and Combinatorics |
DOIs | |
Publication status | E-pub ahead of print - 7 Jun 2019 |
Fingerprint
Cite this
}
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 -