Counting small cycles in generalized de Bruijn digraphs
Toru Hasunuma, Yukio Shibata · Networks · 1997
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 ≤ 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.