Abstract Let T1, T2, …, Tk be spanning trees in a graph G. If for any two vertices u, v in G, the paths from u to v in T1, T2, …, Tk are pairwise internally disjoint, then T1, T2, …, Tk are completely independent spanning trees in G. Completely independent spanning trees can be applied to fault‐tolerant communication problems in interconnection networks. In this article, we show that there are two completely independent spanning trees in any torus network. Besides, we generalize the result for the Cartesian product. In particular, we show that there are two completely independent spanning trees in the Cartesian product of any 2‐connected graphs. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012

Abstract In this paper, we present an upper bound on the pagenumber of an iterated line digraph Lk(G) of a digraph G. Our bound depends only on the digraph G and is independent of the number of iterations k. In particular, it is proved that the pagenumber of Lk(G) does not increase with the number of iterations k. This result generalizes previous results on book‐embeddings of some particular families of iterated line digraphs such as de Bruijn digraphs, Kautz digraphs, and butterfly networks. Also, we apply our result to wrapped butterfly networks. © 2002 Wiley Periodicals, Inc.

In this paper, we count small cycles in generalized de Bruijn digraphs. Let n = pdh, where d ??? p, and gl = gcd(d1 - 1, n). We show that if p < d3 and k ≤ ⌊logd n⌋ + 1, or p > d3 and k ≤ h + 3, then the number of cycles of length k in a generalized de Bruijn digraph GB(n, d) is given by 1/k Σl/k μ(k/l)gl⌈d1/gl⌉, where μ is the Möbius function and ⌈r⌉ denotes the smallest integer not smaller than a real number r. © 1997 John Wiley & Sons, Inc.