ON THE SANDPILE GROUP OF A FAMILY OF GRAPHS
The sandpile group is a subtle isomorphism invariant of a graph and is closely connected with the graph Laplacian matrix. In this paper, the abstract structure of the sandpile group of a family of graphs is determined. It is shown that the sandpile group is always isomorphic to the direct sum of two cyclic groups.
graph, Laplacian matrix, sandpile group, invariant factor, Smith normal form, tree number.
