. We show that the independent spanning tree conjecture on digraphs is true if we restrict ourselves to line digraphs. Also, we construct independent spanning trees with small depths in iterated line digraphs. From the results, we can obtain independent spanning trees with small depths in de Bruijn and Kautz digraphs that improve the previously known upper bounds on the depths. Keywords. independent spanning trees, line digraphs, vertex-connectivity, de Bruijn digraphs, Kautz digraphs, interconnection networks, broadcasting. 1 Introduction Unless stated otherwise each digraph of this paper is nite and may have loops but not multiarcs. Let G be a digraph. Then V (G) and A(G) denote the vertex set and the arc set of G, respectively. Let (u; v) 2 A(G). Then we say that u is adjacent to v, and v is adjacent from u. Also, it is said that (u; v) is incident to v and incident from u. Let (v; w) 2 A(G). Then we say that (u; v) is adjacent to (v; w), and (v; w) is adjacent from (u; v). Let ...

Abstract not found