Inverse graphs associated with finite groups - Monther Rashed Alfuraidan; Yusuf F. Zakariya (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2017)
Let (Γ,*) be a finite group and S a possibly empty subset of Γ containing its non-self-invertible elements. In this paper, we introduce the inverse graph associated with Γ whose set of vertices coincides with Γ such that two distinct vertices u and v are adjacent if and only if either u * vS or v * uS. We then investigate its algebraic and combinatorial structures.