Conjugacy classes of finite groups and graph regularity

cam.issuedOnline	2013-11-05
dc.contributor.author	Bianchi, M
dc.contributor.author	Camina, RD
dc.contributor.author	Herzog, M
dc.contributor.author	Pacifici, E
dc.date.accessioned	2018-12-20T00:31:43Z
dc.date.available	2018-12-20T00:31:43Z
dc.date.issued	2015
dc.description.abstract	Given a finite group $G$, denote by $\Gamma(G)$ the simple undirected graph whose vertices are the distinct sizes of noncentral conjugacy classes of $G$, and set two vertices of $\Gamma(G)$ to be adjacent if and only if they are not coprime numbers. In this note we prove that, if $\Gamma(G)$ is a $k$-regular graph with $k\geq 1$, then $\Gamma(G)$ is a complete graph with $k+1$ vertices.
dc.identifier.doi	10.17863/CAM.34561
dc.identifier.eissn	1435-5337
dc.identifier.issn	0933-7741
dc.identifier.uri	https://www.repository.cam.ac.uk/handle/1810/287254
dc.language.iso	eng
dc.publisher	Walter de Gruyter GmbH
dc.publisher.url	http://dx.doi.org/10.1515/forum-2013-0098
dc.subject	Finite groups
dc.subject	conjugacy class sizes
dc.title	Conjugacy classes of finite groups and graph regularity
dc.type	Article
prism.endingPage	3172
prism.issueIdentifier	6
prism.publicationDate	2015
prism.publicationName	Forum Mathematicum
prism.startingPage	3167
prism.volume	27
rioxxterms.licenseref.startdate	2015-01-01
rioxxterms.licenseref.uri	http://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.type	Journal Article/Review
rioxxterms.version	AM
rioxxterms.versionofrecord	10.1515/forum-2013-0098

Files

Now showing 1 - 1 of 1

Now showing 1 - 1 of 1