Subgroup Graphs of Finite Groups

Ojonugwa Ejima (Usmanu Danfodiyo University, Sokoto, Nigeria.)
Abor Isa Garba (Usmanu Danfodiyo University, Sokoto, Nigeria.)
Kazeem Olalekan Aremu (Usmanu Danfodiyo University, Sokoto, Nigeria.)

International Journal of Applied Sciences and Smart Technologies
Volume 03, Issue 02, December 2021

Let G be a fnite group with the set of subgroups of G denoted by S(G), then the subgroup graphs of G denoted by T(G) is a graph which set of vertices is S(G) such that two vertices H, K in S(G) (H not equal to K)are adjacent if either H is a subgroup of K or K is a subgroup of H. In this paper, we introduce the Subgroupgraphs T associated with G. We investigate some algebraic properties and combinatorial structures of Subgroupgraph T(G) and obtain that the subgroup graph T(G) of G is never bipartite. Further, we show isomorphismand homomorphism of the Subgroup graphs of finite groups.Let  be a finite group with the set of subgroups of  denoted by , then the subgroup graphs of  denoted by is a graph which set of vertices is such that two vertices ,  are adjacent if either  is a subgroup of or   is a subgroup of .  In this paper, we introduce the Subgroup graphs  associated with .  We investigate some algebraic properties and combinatorial structures of Subgroup graph and obtain that the subgroup graph of  is never bipartite. Further, we show isomorphism and homomorphism of the Subgroup graphs of finite groups.