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congruence; digraph; component; height
Let $p$ be a prime. We assign to each positive number $k$ a digraph $G_{p}^{k}$ whose set of vertices is $\{1,2,\ldots ,p-1\}$ and there exists a directed edge from a vertex $a$ to a vertex $b$ if $a^k\equiv b \pmod {p}$. In this paper we obtain a necessary and sufficient condition for $G_{p}^{k_{1}}\simeq G_{p}^{k_{2}}$.
[1] Lucheta, C., Miller, E., Reiter, C.: Digraphs from powers modulo $p$. Fibonacci Quart. 34 (1996), 226-239. MR 1390409 | Zbl 0855.05067
[2] Somer, L., Křížek, M.: On symmetric digraphs of the congruence $x^k\equiv y\pmod{n}$. Discrete Math. 309 (2009), 1999-2009. DOI 10.1016/j.disc.2008.04.009 | MR 2510326
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