ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS

Ashish Kumar Das; Deiborlang Nongsiang

doi:https://doi.org/10.24330/ieja.266195

Article Details

ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS

Authors:

Ashish Kumar Das | Deiborlang Nongsiang

Publisher:

Abdullah HARMANCI

Journal:

International Electronic Journal of Algebra 2016 Vol.19 Issue 19, pp.91-109

Document Type:

Article

Publication Date:

5/2016

Document Language:

Turkish

Document ID (Org No.):

2000718119

Frequency:

Monthly

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.266195

Abstract:

 

The commuting graph of a non-abelian group is a simple graph in
 which the vertices are the non-central elements of the group, and two distinct
 vertices are adjacent if and only if they commute. In this paper, we determine
 (up to isomorphism) all finite non-abelian groups whose commuting graphs are
 acyclic, planar or toroidal. We also derive explicit formulas for the genus of
 the commuting graphs of some well-known class of finite non-abelian groups,
 and show that, every collection of isomorphism classes of finite non-abelian
 groups whose commuting graphs have the same genus is finite.

Article Details

ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS

Authors: Ashish Kumar Das | Deiborlang Nongsiang

Publisher: Abdullah HARMANCI

Journal: International Electronic Journal of Algebra 2016 Vol.19 Issue 19, pp.91-109

Document Type: Article

Publication Date: 5/2016

Document Language: Turkish

Document ID (Org No.): 2000718119

Frequency: Monthly

eISSN: 1306-6048

pISSN: 1306-6048

DOI: https://doi.org/10.24330/ieja.266195

Issues

Authors:

Ashish Kumar Das | Deiborlang Nongsiang

Publisher:

Abdullah HARMANCI

Journal:

International Electronic Journal of Algebra 2016 Vol.19 Issue 19, pp.91-109

Document Type:

Article

Publication Date:

5/2016

Document Language:

Turkish

Document ID (Org No.):

2000718119

Frequency:

Monthly

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.266195