Groups whose non-commuting graph on a transversal is planar or toroidal

摘要

Let G be a finite non-abelian group and let T be a transversal of the center of G. The non-commuting graph of G on a transversal of the center is the graph denoted by ?(G) whose vertices are the non-central elements of T and two vertices x and y are joined by an edge whenever xy≠yx. In this paper, we determine (up to isoclinism) all finite non-abelian groups whose non-commuting graph on a transversal of the center is planar or toroidal.