子群非互素图的平面化

Planarity of the Subgroup Non-coprime Graph

文章主要研究了一类子群非互素图,给出了有限群G的子群非互素图的定义,群G是一个有限群,G的子群非互素图Γ_(2^(G))是以G的非单位真子群为顶点,Γ_(2^(G))中的两个顶点A、B相连当且仅当(|A|,|B|)≠1,通过研究得到有限群的子群非互素图的平面化的充要条件。

A type of subgroup non-coprime graphs is studied,and the definition of subgroup non-coprime graph of finite group G is made.The group G is a finite group,whose subgroup non-coprime graph Γ_(2^(G)) is taking G’s nonunit proper subgroup as vertex with two vertices A,B connected when and only when(|A|,|B|)≠1.The necessary and sufficient conditions for the planarity of the subgroup non-coprime graph of a finite group are obtained through the study.