Let G be a finite group. In this paper we introduce the generalized conjugate graph c(G;n) which is a graph whose vertices are, all the non-central subsets of G with n elements and two distinct vertices X and Y join by an edge if X = Y g for some g 2 G. We present a condition under which two generalized conjugate graph are isomorphic. Moreover, this graph is a key to dene the probability that two subsets of the group G with the same cardinality be conjugate.

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