Isomorphic factorization, the Kronecker product and the line digraph

Authors:
Yuuki Tanaka;Hiroyuki Kawai;Yukio Shibata
Affiliations:
Advanced Technology Research Center, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma 376-8515, Japan;Department of Computer Engineering, Hakodate National College of Technology, 14-1 Tokura-cho, Hakodate, Hokkaido 042-8501, Japan;Department of Computer Science, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma 376-8515, Japan
Venue:
Information Processing Letters
Year:
2007

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Abstract

In this paper, we investigate isomorphic factorizations of the Kronecker product graphs. Using these relations, it is shown that (1) the Kronecker product of the d-out-regular digraph and the complete symmetric digraph is factorized into the line digraph, (2) the Kronecker product of the Kautz digraph and the de Bruijn digraph is factorized into the Kautz digraph, (3) the Kronecker product of binary generalized de Bruijn digraphs is factorized into the binary generalized de Bruijn digraph.