Inverse graphs associated with finite groups - Monther Rashed Alfuraidan; Yusuf F. Zakariya (Electronic Journal of Graph Theory and Applications (EJGTA), 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 $u * v\in S$ or $v * u\in S$. We then investigate its algebraic and combinatorial structures.