On the number of cycles in generalized Kautz digraphs
نویسندگان
چکیده
In this paper, we count cycles in a generalized Kautz digraph GK (n; d). Let n = pd such that d| ,p. Also let gl = gcd(d − (−1)l; n). We show that if one of the following conditions holds: • p6 √ d7 d+1 and k6 logd n+ 1, • √ d7 d+1 ¡p¡d (d+ 1) and k6 logd ( n 3 √ p2(d+1) ) + 10 3 , • d(d+ 1)¡p and k6 logd ( n d+1 ) then the number of cycles of length k in GK (n; d) is given by 1 k ∑ l | k ( k l ) (d + (−1)(gl − 1)); where is the M9 obius function. c © 2004 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 285 شماره
صفحات -
تاریخ انتشار 2004