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 $𝕋(G)$ whose vertices are the non-central elements of $T$ and two vertices $x$ and $y$ are joined by an edge whenever $xy\ne yx$. 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.

中文翻译：

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横向上的非对易图是平面或环形的组

让$G$是一个有限的非阿贝尔群并且让$吨$是中心的横向$G$. 非通勤图$G$在中心的横截面上是表示为的图$𝕋(G)$其顶点是非中心元素$吨$和两个顶点$X$和$\mathrm{是的}$任何时候都由一条边连接$X\mathrm{是的}\ne \mathrm{是的}X$. 在本文中，我们确定（直到等斜）所有在中心的横向上的非对易图是平面或环形的有限非阿贝尔群。