Generalized non-coprime graphs of groups

Let G be a finite group with identity e and H ≠ { e } be a subgroup of G . The generalized non-coprime graph Γ G , H of G with respect to H is the simple undirected graph with G \ { e } as the vertex set and two distinct vertices x and y are adjacent if and only if gcd ( | x | , | y | ) ≠ 1 and eith...

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