Abstract
The paper extends the results given by M. Křížek and L. Somer, On a connection of number theory with graph theory, Czech. Math. J. 54 (129) (2004), 465–485 (see [5]). For each positive integer n define a digraph Γ(n) whose set of vertices is the set H = {0, 1, ..., n − 1} and for which there is a directed edge from a ∈ H to b ∈ H if a 3 ≡ b (mod n). The properties of such digraphs are considered. The necessary and the sufficient condition for the symmetry of a digraph Γ(n) is proved. The formula for the number of fixed points of Γ(n) is established. Moreover, some connection of the length of cycles with the Carmichael λ-function is presented.
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Skowronek-Kaziów, J. Properties of digraphs connected with some congruence relations. Czech Math J 59, 39–49 (2009). https://doi.org/10.1007/s10587-009-0003-9
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DOI: https://doi.org/10.1007/s10587-009-0003-9