The stable subgroup graph

The stable subgroup graph

Blog Article

In this paper we introduce stable subgroup graph associated to the group $G$.It is a Swim graph with vertex set all subgroups of $G$ and two distinct subgroups $H_1$ and $H_2$ are adjacent if $St_{G}(H_1)cap H_2 eq 1$ or $St_{G}(H_2)cap H_1 eq 1$.Its planarity is discussed whenever $G$ is an abelian group, $p$-group, nilpotent, Gift Card supersoluble or soluble group.

Finally, the induced subgraph of stable subgroup graph with vertex set whole non-normal subgroups is considered and its planarity is verified for some certain groups.