Structure of digraphs associated with quadratic congruences with composite moduli.(English)Zbl 1161.05323
Summary: We assign to each positive integer \(n\) a digraph \(G(n)\) whose set of vertices is \(H=\{0,1,\dots,n-1\}\) and for which there exists a directed edge from \(a\in H\) to \(b\in H\) if \(a^2\equiv b\pmod n\). Associated with \(G(n)\) are two disjoint subdigraphs: \(G_1(n)\) and \(G_2(n)\) whose union is \(G(n)\). The vertices of \(G_1(n)\) correspond to those residues which are relatively prime to \(n\). The structure of \(G_1(n)\) is well understood. In this paper, we investigate in detail the structure of \(G_2(n)\).
MSC:
| 05C20 | Directed graphs (digraphs), tournaments |
| 05C62 | Graph representations (geometric and intersection representations, etc.) |
Keywords:
digraphsCite
Full Text:DOI
References:
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