The geometries, the stabilities, and the electronic properties of Run Au and Run (n=112) clusters are systematically investigated by the density functional theory. The results suggest that the lowest energy structures for Run Au clusters can be obtained by substituting one Ru atom in Run+1 clusters with Au atom. The geometries of Run Au clusters are similar to those of Run+1 clusters except local structural distortions. The second-order difference and fragmentation energy show that Ru5, Ru8, Ru5Au, and Ru8Au clusters are the most stable among these studied clusters, the doped Au atoms do not change the relative stabilities of Run clusters; the Au impurities increase the chemical activities of Run clusters, and the value of gap is determined mainly by the electron-pairing effect; the doped Au atoms increase the total magnetic moments of Run Au in most cases.