Classification of Arc-Transitive Elementary Abelian Covers of the C13 Graph

Qianru Xiao; Aysha Khan; Narges Mehdipoor; Ali Asghar Talebi

doi:10.3390/sym14051066

Classification of Arc-Transitive Elementary Abelian Covers of the C13 Graph

Qianru Xiao
, Aysha Khan
, Narges Mehdipoor
, Ali Asghar Talebi

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let Γ be a graph and G ≤ Aut(Γ). A graph Γ can be called G-arc-transitive (GAT) if G acts transitively on its arc set. A regular covering projection p: Γ → Γ is arc-transitive (AT) if an AT subgroup of Aut(Γ) lifts under p. In this study, by applying a number of concepts in linear algebra such as invariant subspaces (IVs) of matrix groups (MGs), we discuss regular AT elementary abelian covers (R-AT-EA-covers) of the C13 graph.

Original language	English
Article number	1066
Journal	Symmetry
Volume	14
Issue number	5
DOIs	https://doi.org/10.3390/sym14051066
State	Published - May 2022

Keywords

AT graphs
C13 graph
homology group
IVs
lifting automorphisms
MGs
regular covering

Access to Document

10.3390/sym14051066

Cite this

@article{ed0239f9fbd04ea7af27aa184257782a,

title = "Classification of Arc-Transitive Elementary Abelian Covers of the C13 Graph",

abstract = "Let Γ be a graph and G ≤ Aut(Γ). A graph Γ can be called G-arc-transitive (GAT) if G acts transitively on its arc set. A regular covering projection p: Γ → Γ is arc-transitive (AT) if an AT subgroup of Aut(Γ) lifts under p. In this study, by applying a number of concepts in linear algebra such as invariant subspaces (IVs) of matrix groups (MGs), we discuss regular AT elementary abelian covers (R-AT-EA-covers) of the C13 graph.",

keywords = "AT graphs, C13 graph, homology group, IVs, lifting automorphisms, MGs, regular covering",

author = "Qianru Xiao and Aysha Khan and Narges Mehdipoor and Talebi, \{Ali Asghar\}",

note = "Publisher Copyright: {\textcopyright} 2022 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2022",

month = may,

doi = "10.3390/sym14051066",

language = "English",

volume = "14",

journal = "Symmetry",

issn = "2073-8994",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "5",

}

TY - JOUR

T1 - Classification of Arc-Transitive Elementary Abelian Covers of the C13 Graph

AU - Xiao, Qianru

AU - Khan, Aysha

AU - Mehdipoor, Narges

AU - Talebi, Ali Asghar

PY - 2022/5

Y1 - 2022/5

N2 - Let Γ be a graph and G ≤ Aut(Γ). A graph Γ can be called G-arc-transitive (GAT) if G acts transitively on its arc set. A regular covering projection p: Γ → Γ is arc-transitive (AT) if an AT subgroup of Aut(Γ) lifts under p. In this study, by applying a number of concepts in linear algebra such as invariant subspaces (IVs) of matrix groups (MGs), we discuss regular AT elementary abelian covers (R-AT-EA-covers) of the C13 graph.

AB - Let Γ be a graph and G ≤ Aut(Γ). A graph Γ can be called G-arc-transitive (GAT) if G acts transitively on its arc set. A regular covering projection p: Γ → Γ is arc-transitive (AT) if an AT subgroup of Aut(Γ) lifts under p. In this study, by applying a number of concepts in linear algebra such as invariant subspaces (IVs) of matrix groups (MGs), we discuss regular AT elementary abelian covers (R-AT-EA-covers) of the C13 graph.

KW - AT graphs

KW - C13 graph

KW - homology group

KW - IVs

KW - lifting automorphisms

KW - MGs

KW - regular covering

UR - https://www.scopus.com/pages/publications/85134424453

U2 - 10.3390/sym14051066

DO - 10.3390/sym14051066

M3 - Article

AN - SCOPUS:85134424453

SN - 2073-8994

VL - 14

JO - Symmetry

JF - Symmetry

IS - 5

M1 - 1066

ER -

Classification of Arc-Transitive Elementary Abelian Covers of the C13 Graph

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this