0380313 - MÚ 2013 RIV US eng J - Journal Article
Somer, L. - Křížek, Michal
Power digraphs modulo n are symmetric of order M in and only if M is square free.
Fibonacci Quarterly. Roč. 50, č. 3 (2012), s. 196-206. ISSN 0015-0517. E-ISSN 0015-0517
R&D Projects: GA AV ČR(CZ) IAA100190803
Institutional support: RVO:67985840
Keywords : symmetric iteration digraphs
Subject RIV: BA - General Mathematics
Result website:
http://www.fq.math.ca/Abstracts/50-3/somer.pdf

We assign to each pair of positive integers k>=2 and n a digraph G(n,k) whose set of vertices is H = {0, 1, . . . , n − 1} and for which there is a directed edge from a H to b H if ak = b (mod n). The digraph G(n, k) is symmetric of order M if its set of components can be partitioned into disjoint subsets, each containing exactly M isomorphic components. Deng and Yuan completely characterized all symmetric digraphs of order M when M = 2 or M is divisible by an odd prime. We demonstrate that their classification is complete by showing that there are no symmetric digraphs G(n, k) of order 2s for s >= 2.
Permanent Link: http://hdl.handle.net/11104/0211051