Geodesic
Isomorphic digraphs from powers modulo $p$
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 771-779 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $G_{p}^{k_{1}}\simeq G_{p}^{k_{2}}$.
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 $G_{p}^{k_{1}}\simeq G_{p}^{k_{2}}$.
DOI : 10.1007/s10587-011-0025-y
Classification : 05C20, 05C38, 11A15
Keywords: congruence; digraph; component; height 
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     pages = {771--779},
     year = {2011},
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Deng, Guixin; Yuan, Pingzhi. Isomorphic digraphs from powers modulo $p$. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 771-779. doi: 10.1007/s10587-011-0025-y

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