  We study the scaling properties of the clusters grown by the Wolff algorithm
on seven different Sierpinski-type fractals of Hausdorff dimension $1 < d_f \le
3$ in the framework of the Ising model. The mean absolute value of the surface
energy of Wolff cluster follows a power law with respect to the lattice size.
Moreover, we investigate the probability density distribution of the surface
energy of Wolff cluster and are able to establish a new scaling relation. It
enables us to introduce a new exponent associated to the surface energy of
Wolff cluster. Finally, this new exponent is linked to a dynamical exponent via
an inequality.
