The essence of the non-commuting graph remind us to find a connection between this graph and the commutativity degree as denoted by d(G). On the other hand, d(H, G) the relative commutativity degree, was the key to generalize the non-commuting graph Γ_G to the relative non-commuting graph (denoted by Γ_H, _G) for a non-abelian group G and a subgroup H of G. In this paper, we give some results about Γ_H, _G which are mostly new. Furthermore, we prove that if (H_1, G_1) and (H_2, G_2) are relative isoclinic then ΓH_1, G_1 ? Γ H_2, G_2 under special conditions.
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