子群非互素图的连通性

Connectivity 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Γ2G。为以G的非单位真子群为顶点,Γ2G中的两个顶点A,B相连当且仅当(|A|,|S|)≠1。通过研究得到有限群的子群非互素图的连通性的条件。

A class of connectivity of the subgroup non-coprime graph is studied in the paper and the definition of subgroups of finite group G is given.G is a finite group,whose subgroup non-coprime graph Γ2G is the graph with vertices of the non-identity proper subgroup and two distinct vertices A and B adjacent when(|A|,|B|)≠1.Thus the conditions for the connectivity of the subgroups of finite groups are obtained.