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

0360532 - MÚ 2012 RIV CZ eng J - Článek v odborném periodiku
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
Grant CEP: GA AV ČR(CZ) IAA100190803
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: Sophie Germain primes * Fermat primes * primitive roots * Chinese Remainder Theorem * congruence * diagraphs
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.262, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0198051