Semisymmetric \(Z_{p}\)-covers of the \(C20\) graph
A graph \(X\) is said to be \(G\)-semisymmetric if it is regular and there exists a subgroup \(G\) of \(A := \operatorname{Aut}(X)\) acting transitively on its edge set but not on its vertex set. In the case of \(G = A\), we call \(X\) a semisymmetric graph. Finding elementary abelian covering proje...
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Lugansk National Taras Shevchenko University
2021
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admjournalluguniveduua-article-2522021-07-19T08:39:30Z Semisymmetric \(Z_{p}\)-covers of the \(C20\) graph Talebi, A. A. Mehdipoor, N. invariant subspaces, homology group, $C20$ graph, semisymmetric graphs, regular covering, lifting automorphisms 05C25, 20b25 A graph \(X\) is said to be \(G\)-semisymmetric if it is regular and there exists a subgroup \(G\) of \(A := \operatorname{Aut}(X)\) acting transitively on its edge set but not on its vertex set. In the case of \(G = A\), we call \(X\) a semisymmetric graph. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields. In this study, by applying concept linear algebra, we classify the connected semisymmetric \(z_{p}\)-covers of the \(C20\) graph. Lugansk National Taras Shevchenko University 2021-07-19 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/252 10.12958/adm252 Algebra and Discrete Mathematics; Vol 31, No 2 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/252/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/252/817 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/252/819 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/252/834 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/252/835 Copyright (c) 2021 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2021-07-19T08:39:30Z |
| collection |
OJS |
| language |
English |
| topic |
invariant subspaces homology group $C20$ graph semisymmetric graphs regular covering lifting automorphisms 05C25 20b25 |
| spellingShingle |
invariant subspaces homology group $C20$ graph semisymmetric graphs regular covering lifting automorphisms 05C25 20b25 Talebi, A. A. Mehdipoor, N. Semisymmetric \(Z_{p}\)-covers of the \(C20\) graph |
| topic_facet |
invariant subspaces homology group $C20$ graph semisymmetric graphs regular covering lifting automorphisms 05C25 20b25 |
| format |
Article |
| author |
Talebi, A. A. Mehdipoor, N. |
| author_facet |
Talebi, A. A. Mehdipoor, N. |
| author_sort |
Talebi, A. A. |
| title |
Semisymmetric \(Z_{p}\)-covers of the \(C20\) graph |
| title_short |
Semisymmetric \(Z_{p}\)-covers of the \(C20\) graph |
| title_full |
Semisymmetric \(Z_{p}\)-covers of the \(C20\) graph |
| title_fullStr |
Semisymmetric \(Z_{p}\)-covers of the \(C20\) graph |
| title_full_unstemmed |
Semisymmetric \(Z_{p}\)-covers of the \(C20\) graph |
| title_sort |
semisymmetric \(z_{p}\)-covers of the \(c20\) graph |
| description |
A graph \(X\) is said to be \(G\)-semisymmetric if it is regular and there exists a subgroup \(G\) of \(A := \operatorname{Aut}(X)\) acting transitively on its edge set but not on its vertex set. In the case of \(G = A\), we call \(X\) a semisymmetric graph. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields. In this study, by applying concept linear algebra, we classify the connected semisymmetric \(z_{p}\)-covers of the \(C20\) graph. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2021 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/252 |
| work_keys_str_mv |
AT talebiaa semisymmetriczpcoversofthec20graph AT mehdipoorn semisymmetriczpcoversofthec20graph |
| first_indexed |
2025-12-02T15:39:58Z |
| last_indexed |
2025-12-02T15:39:58Z |
| _version_ |
1850411580546613248 |