  We generalize a theorem of Knuth relating the oriented spanning trees of a
directed graph G and its directed line graph LG. The sandpile group is an
abelian group associated to a directed graph, whose order is the number of
oriented spanning trees rooted at a fixed vertex. In the case when G is regular
of degree k, we show that the sandpile group of G is isomorphic to the quotient
of the sandpile group of LG by its k-torsion subgroup. As a corollary we
compute the sandpile groups of two families of graphs widely studied in
computer science, the de Bruijn graphs and Kautz graphs.
