Completely independent spanning trees in the underlying graph of a line digraph

In this note, we define completely independent spanning trees. We say that T-1,T-2,...,T-k are completely independent spanning trees in a graph H if for any vertex r of H, they are independent spanning trees rooted at r. We present a characterization of completely independent spanning trees. Also, we show that for any k-vertex-connected line digraph L(G), there are k completely independent spanning trees in the underlying graph of L(G). At last, we apply our results to de Bruijn graphs, Kautz graphs, and wrapped butterflies. (C) 2001 Elsevier Science B.V. All rights reserved.