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 Gamma_{G} to the relative non-commuting graph (denoted by Gamma_{H,G} ) for a non-abelian group G and a subgroup H of G . In this paper, we give some results about Gamma_{H,G} which are mostly new. Furthermore, we prove that if (H_{1},G_{1}) and (H_{2},G_{2}) are relative isoclinic then Gamma_{H_{1},G_{1}} cong Gamma_{H_{2},G_{2}} under special conditions.

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