Abstract
In the first part, we assign to each positive integer n a digraph Γ(n, 5), whose set of vertices consists of elements of the ring ℤ n = {0, 1, …, n − 1} with the addition and the multiplication operations modulo n, and for which there is a directed edge from a to b if and only if a 5 ≡ b (mod n). Associated with Γ(n, 5) are two disjoint subdigraphs: Γ1(n, 5) and Γ2(n, 5) whose union is Γ(n, 5). The vertices of Γ1(n, 5) are coprime to n, and the vertices of Γ2(n, 5) are not coprime to n. In this part, we study the structure of Γ(n, 5) in detail.
In the second part, we investigate the zero-divisor graph G(ℤ n ) of the ring ℤ n . Its vertex- and edge-connectivity are discussed.
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The research has been supported by the NSFC Grant 11271208.
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Ju, T., Wu, M. On iteration digraph and zero-divisor graph of the ring ℤ n . Czech Math J 64, 611–628 (2014). https://doi.org/10.1007/s10587-014-0122-9
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DOI: https://doi.org/10.1007/s10587-014-0122-9