Embedding iterated line digraphs in books

Abstract

In this paper, we present an upper bound on the pagenumber of an iterated line digraph L k (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 L k (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.

On the Pagenumber of the Cube-Connected Cycles

“…A 3-page book embedding of CCC(4) mapping is injective for vertices of level n − 2 or n − 1. For vertices u =(t; x), v = (s; y) where s and t are n − 2 or n − 1, if x = y, |2B(x) − 2B(y)| ≥ 2 and n−1 i=0 x i is at most one, then ψ o…”

Laying Out Iterated Line Digraphs Using Queues

“…-Stacknumber: complete graphs [4], complete bipartite graphs [24], butterfly graphs [12], trees, grids, X-trees [5], hypercubes [5,22], de Bruijn digraphs, Kautz digraphs, shuffle-exchange graphs [16], planar graphs [32], genus-g graphs [23], bandwidth-k graphs [28], k-trees [13], iterated line digraphs [14]. -Queuenumber: complete graphs, complete bipartite graphs, trees, grids, unicyclic graphs, X-trees, binary de Bruijn graphs, butterfly graphs (all in [21]), k-tree [6,26,31],…”

Embedding Sun Graphs in a Single Page

“…The book embeddings have been studied for many classes of graphs. To name a few, we have: Complete Graphs [1,2], Complete Bipartite Graphs [10], Trees, Grids and X-trees [3], hypercubes [3,9], incomplete hypercubes [8], iterated line digraphs [6], de Bruijn graphs, Kautz graphs, shuffle-exchange graphs [7], for each of which embedding in books have been studied.…”