$Double-toroidal and $1$-planar non-commuting graph of a group$

Double-toroidal and $1$-planar non-commuting graph of a group

Let $G$ be a finite non-abelian group and denote by $Z(G)$ its center. The non-commuting graph of $G$ on a transversal of the center is the graph whose vertices are the non-central elements of a transversal of $Z(G)$ in $G$ and two vertices $x$ and $y$ are adjacent whenever \(xy\neq yx...

Full description

Saved in:

Bibliographic Details
Date:	2023
Main Author:	Pezzott, J. C. M.
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2023
Subjects:	non-commuting graph double-toroidal graph $1$-planar graph isoclinism 05C25 05C10
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1935
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Algebra and Discrete Mathematics

Institution

Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-1935
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua:article-19352023-02-08T16:55:57Z Double-toroidal and $1$-planar non-commuting graph of a group Pezzott, J. C. M. non-commuting graph, double-toroidal graph, $1$-planar graph, isoclinism 05C25, 05C10 Let $G$ be a finite non-abelian group and denote by $Z(G)$ its center. The non-commuting graph of $G$ on a transversal of the center is the graph whose vertices are the non-central elements of a transversal of $Z(G)$ in $G$ and two vertices $x$ and $y$ are adjacent whenever $xy\neq yx$. In this work, we classify the finite non-abelian groups whose non-commuting graph on a transversal of the center is double-toroidal or $1$-planar. Lugansk National Taras Shevchenko University 2023-02-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1935 10.12958/adm1935 Algebra and Discrete Mathematics; Vol 34, No 1 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1935/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1935/958 Copyright (c) 2023 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2023-02-08T16:55:57Z
collection	OJS
language	English
topic	non-commuting graph double-toroidal graph $1$-planar graph isoclinism 05C25 05C10
spellingShingle	non-commuting graph double-toroidal graph $1$-planar graph isoclinism 05C25 05C10 Pezzott, J. C. M. Double-toroidal and $1$-planar non-commuting graph of a group
topic_facet	non-commuting graph double-toroidal graph $1$-planar graph isoclinism 05C25 05C10
format	Article
author	Pezzott, J. C. M.
author_facet	Pezzott, J. C. M.
author_sort	Pezzott, J. C. M.
title	Double-toroidal and $1$-planar non-commuting graph of a group
title_short	Double-toroidal and $1$-planar non-commuting graph of a group
title_full	Double-toroidal and $1$-planar non-commuting graph of a group
title_fullStr	Double-toroidal and $1$-planar non-commuting graph of a group
title_full_unstemmed	Double-toroidal and $1$-planar non-commuting graph of a group
title_sort	double-toroidal and $1$-planar non-commuting graph of a group
description	Let $G$ be a finite non-abelian group and denote by $Z(G)$ its center. The non-commuting graph of $G$ on a transversal of the center is the graph whose vertices are the non-central elements of a transversal of $Z(G)$ in $G$ and two vertices $x$ and $y$ are adjacent whenever $xy\neq yx$. In this work, we classify the finite non-abelian groups whose non-commuting graph on a transversal of the center is double-toroidal or $1$-planar.
publisher	Lugansk National Taras Shevchenko University
publishDate	2023
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1935
work_keys_str_mv	AT pezzottjcm doubletoroidaland1planarnoncommutinggraphofagroup
first_indexed	2025-07-17T10:32:28Z
last_indexed	2025-07-17T10:32:28Z
_version_	1837889852002009088

Double-toroidal and \(1\)-planar non-commuting graph of a group

Institution

Similar Items