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Counting closed walks in generalized de Bruijn graphs

✍ Scribed by Yukio Shibata; Miyuki Shirahata; Shingo Osawa

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
313 KB
Volume
49
Category
Article
ISSN
0020-0190

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πŸ“œ SIMILAR VOLUMES

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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

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## Abstract The generalized de Bruijn digraph __G__~__B__~(__n__,__m__) is the digraph (__V__,__A__) where __V__ = {0, 1,…,__m__ βˆ’ 1} and (__i__,__j__) ∈ __A__ if and only if __j__ ≑ __i____n__+__Ξ±__ (mod __m__) for some __Ξ±__ ∈ {0, 1, 2,…,__n__βˆ’ 1}. By replacing each arc of __G__~__B__~(__n__,__m_