2004年8月

# On the number of cycles in generalized Kautz digraphs

DISCRETE MATHEMATICS
• T Hasunuma
• ,
• Y Kikuchi
• ,
• T Mori
• ,
• Y Shibata

285
1-3

127

140

DOI
10.1016/j.disc.2004.01.014

ELSEVIER SCIENCE BV

In this paper, we count cycles in a generalized Kautz digraph G(K)(n,d). Let n=pd(h) such that d/p. Also let g(l)=gcd(d(l)-(-1)(l),n). We show that if one of the following conditions holds:
pless than or equal torootd(7)/d+1 and kless than or equal tolog(d) n+1,
rootd(7)/d+1 &lt;p&lt;d(5)(d+1) and kless than or equal tolog(d) (n/(3)rootp(2)(d+1)
d(5)(d+1 &lt;p and k&LE;log(d) (n/d+1)
then the number of cycles of length k in G(K)(n,d) is given by
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