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Hypercubes, shuffle-exchange graphs and de Bruijn digraphs

✍ Scribed by Niall Graham; Frank Harary


Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
438 KB
Volume
17
Category
Article
ISSN
0895-7177

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In this paper, we count small cycles in generalized de Bruijn digraphs. Let n Γ… pd h , where d Γ‰ / p, and g l Γ… gcd(d l 0 1, n). We show that if p Γ΅ d 3 and k Β°ο£°log d nο£» / 1, or p ΓΊ d 3 and k Β°h / 3, then the number of cycles of length k in a generalized de Bruijn digraph G B (n, d) is given by 1/ k