The structure of digraphs associated with the congruence Xk=y(mod n)

0360532 - MÚ 2012 RIV CZ eng J - Journal Article
Somer, L. - Křížek, Michal
The structure of digraphs associated with the congruence Xk=y(mod n).
Czechoslovak Mathematical Journal. Roč. 61, č. 2 (2011), s. 337-358. ISSN 0011-4642. E-ISSN 1572-9141
R&D Projects: GA AV ČR(CZ) IAA100190803
Institutional research plan: CEZ:AV0Z10190503
Keywords : Sophie Germain primes * Fermat primes * primitive roots * Chinese Remainder Theorem * congruence * diagraphs
Subject RIV: BA - General Mathematics
Impact factor: 0.262, year: 2011
http://www.springerlink.com/content/0734x49116250643/

We assign to each pair of positive integers n and k > 2 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 2 H to b 2 H if ak b (mod n). We investigate the structure of G(n, k). In particular, upper bounds are given for the longest cycle in G(n, k). We find subdigraphs of G(n, k), called fundamental constituents of G(n, k), for which all trees attached to cycle vertices are isomorphic.
Permanent Link: http://hdl.handle.net/11104/0198051