On the sandpile group of the graph K3×Cn

The sandpile group of a graph is a refinement of the number of spanning trees of the graph and is closely connected with the graph Laplacian matrix. In this paper, the structure of the sandpile group on the graph K3×Cn is determined and it is shown that the Smith normal form of the sandpile group of K3×Cn is always the direct sum of four or five cyclic groups. Our methods can be generated to the graphs K4×Cn and K5×Cn.