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The commuting graph of an arbitrary ring R,denoted by T(R),is a graph whose vertices are all non-central elements of R,and two distinct vertices a and b are adjacent if and only if ab =ba.In this paper,we investigate the connectivity and the diameter of Γ(ZnS3).We show that Γ(ZnS3) is connected if and only if n is not a prime number.If Γ(ZnS3) is connected then diam(Γ(ZnS3)) =3,while if Γ(ZnS3) is disconnected then every connected component of Γ(ZnS3) must be a complete graph with same size,and we completely determine the vertice set of every connected component.