On symmetric digraphs of the congruence x.sup.k./sup. = y(mod n)

0323492 - MÚ 2009 RIV NL eng J - Journal Article
Somer, L. - Křížek, Michal
On symmetric digraphs of the congruence x^k = y(mod n).
[O symetrických orientovaných grafech kongruence x^k = y (mod n).]
Discrete Mathematics. Roč. 309, č. 10 (2009), s. 1999-2009. ISSN 0012-365X. E-ISSN 1872-681X
R&D Projects: GA AV ČR(CZ) IAA100190803; GA MŠMT 1P05ME749
Institutional research plan: CEZ:AV0Z10190503
Keywords : chinese remainder theorem * congruence * symmetric digraphs
Subject RIV: BA - General Mathematics
Impact factor: 0.548, year: 2009

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 .. H to b .. H if a^k= b (mod n). The digraph G(n,k) is symmetric of order M if its set of components can be partitioned into subsets of size M with each subset containing M isomorphic components. We generalize earlier theorems by Szalay, Carlip, and Mincheva on symmetric digraphs G(n,2) of order 2 to symmetric digraphs G(n,k) of order M when k > 2 is arbitrary

V článku zobecňujeme některá známá tvrzení pro kvadratické kongruence, které odpovídají symetrickým orientovaným grafům, na případ k > 2.
Permanent Link: http://hdl.handle.net/11104/0171431