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The structure of digraphs associated with the congruence Xk=y(mod n)
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SYSNO ASEP 0360532 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The structure of digraphs associated with the congruence Xk=y(mod n) Author(s) Somer, L. (US)
Křížek, Michal (MU-W) RID, SAI, ORCIDSource Title Czechoslovak Mathematical Journal. - : Springer - ISSN 0011-4642
Roč. 61, č. 2 (2011), s. 337-358Number of pages 22 s. Language eng - English Country CZ - Czech Republic Keywords Sophie Germain primes ; Fermat primes ; primitive roots ; Chinese Remainder Theorem ; congruence ; diagraphs Subject RIV BA - General Mathematics R&D Projects IAA100190803 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000300091600005 EID SCOPUS 84856752091 DOI 10.1007/s10587-011-0079-x Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2012
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