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

#### Ashish Kumar Das [1] , Deiborlang Nongsiang [2]

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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.
Commuting graph, finite group, AC-group, genus of the commuting graphs
Konular JA57HS68AS Makaleler Yazar: Ashish Kumar Das Yazar: Deiborlang Nongsiang
 Bibtex @ { ieja266195, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2016}, volume = {19}, pages = {91 - 109}, doi = {10.24330/ieja.266195}, title = {ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS}, key = {cite}, author = {Nongsiang, Deiborlang and Das, Ashish Kumar} } APA Das, A , Nongsiang, D . (2016). ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS. International Electronic Journal of Algebra, 19 (19), 91-109. DOI: 10.24330/ieja.266195 MLA Das, A , Nongsiang, D . "ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS". International Electronic Journal of Algebra 19 (2016): 91-109 Chicago Das, A , Nongsiang, D . "ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS". International Electronic Journal of Algebra 19 (2016): 91-109 RIS TY - JOUR T1 - ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS AU - Ashish Kumar Das , Deiborlang Nongsiang Y1 - 2016 PY - 2016 N1 - doi: 10.24330/ieja.266195 DO - 10.24330/ieja.266195 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 91 EP - 109 VL - 19 IS - 19 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266195 UR - http://dx.doi.org/10.24330/ieja.266195 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS %A Ashish Kumar Das , Deiborlang Nongsiang %T ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS %D 2016 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 19 %N 19 %R doi: 10.24330/ieja.266195 %U 10.24330/ieja.266195 ISNAD Das, Ashish Kumar , Nongsiang, Deiborlang . "ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS". International Electronic Journal of Algebra 19 / 19 (Haziran 2016): 91-109. http://dx.doi.org/10.24330/ieja.266195