根据互素图的端顶点数对群进行分类
Classification of Groups according to the number of end vertices in the coprime graph
摘要：
本文根据相伴互质图的端顶点数刻画群。得到了依赖于端顶点数的群的阶的上界。我们还证明了$2-$群是唯一一个互质图的端点数为奇数的群。给出了互素图中端点数较少的群的分类。其中一个结果表明，$\mathbb{Z}_4$和$\mathbb{Z}_2\times \mathbb{Z}_2$是唯一的互质图恰好有三个端点的群。
英文摘要：
In this paper we characterize groups according to the number of end vertices in the associated coprime graphs. An upper bound on the order of the group that depends on the number of end vertices is obtained. We also prove that $2-$groups are the only groups whose coprime graphs have odd number of end vertices. Classifications of groups with small number of end vertices in the coprime graphs are given. One of the results shows that $\mathbb{Z}_4$ and $\mathbb{Z}_2\times \mathbb{Z}_2$ are the only groups whose coprime graph has exactly three end vertices.
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