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

Ashish Kumar Das, Deiborlang Nongsiang
2016 International Electronic Journal of Algebra  
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
more » ... ction of isomorphism classes of finite non-abelian groups whose commuting graphs have the same genus is finite. (2010) : 20D60, 05C25 Mathematics Subject Classification
doi:10.24330/ieja.266195 fatcat:nkxgzsug4zekvf7hztpozdsupu