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Let G be a k₀-connected graph ,and let , ,be the w- width distance between the two vertices  u,v  in G. The w-Wiener polynomial of the width distance of G is defined by:       The w-Wiener polynomials of the square of a path , the square of a cycle  ,and of an m-cube  are obtained in this paper . The diameter with respect to the width distance –w ,and the Wiener index for each such graphs are also obtained .