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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 ∈ S or v * u ∈ S. We then investigate its algebraic and combinatorial structures.doi:10.5614/ejgta.2017.5.1.14 fatcat:hqq2jvorh5blrn76lpgnpwbcnm