Suppose n is a fxed positive integer. We introduce the relative n-th non-commuting graph n H;G, associated to the non-abelian subgroup H of group G. The vertex set is G n Cn H;G in which Cn H;G = fx 2 G : [x; yn] = 1 and [xn; y] = 1 for all y 2 Hg. Moreover, fx; yg is an edge if x or y belong to H and xyn = ynx or xny = yxn. In fact, the relative n-th commutativity degree, Pn(H;G) the probability that n-th power of an element of the sub- group H commutes with another random element of the group G and the non-commuting graph are the keys to construct such a graph. It is proved that two isoclinic non-abelian groups have iso- morphic graphs under special conditions.

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