Structure of cubic mapping graphs for the ring of Gaussian integers modulo $n$

Yangjiang Wei; Jizhu Nan; Gaohua Tang

Displaying similar documents to “Structure of cubic mapping graphs for the ring of Gaussian integers modulo $n$ ”

Isomorphic digraphs from powers modulo $p$

Guixin Deng, Pingzhi Yuan (2011)

Czechoslovak Mathematical Journal

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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 ${1, 2, ..., p - 1}$ and there exists a directed edge from a vertex $a$ to a vertex $b$ if $a^{k} \equiv b (mod p)$ . In this paper we obtain a necessary and sufficient condition for $G_{p}^{k_{1}} ≃ G_{p}^{k_{2}}$ .

Characterization of power digraphs modulo $n$

Uzma Ahmad, Syed Husnine (2011)

Commentationes Mathematicae Universitatis Carolinae

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A power digraph modulo $n$ , denoted by $G (n, k)$ , is a directed graph with $Z_{n} = {0, 1, \dots, n - 1}$ as the set of vertices and $E = {(a, b) : a^{k} \equiv b (mod n)}$ as the edge set, where $n$ and $k$ are any positive integers. In this paper we find necessary and sufficient conditions on $n$ and $k$ such that the digraph $G (n, k)$ has at least one isolated fixed point. We also establish necessary and sufficient conditions on $n$ and $k$ such that the digraph $G (n, k)$ contains exactly two components. The primality of Fermat number is also discussed.

The cubic mapping graph for the ring of Gaussian integers modulo $n$

Yangjiang Wei, Jizhu Nan, Gaohua Tang (2011)

Czechoslovak Mathematical Journal

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The article studies the cubic mapping graph $Γ (n)$ of $ℤ_{n} [i]$ , the ring of Gaussian integers modulo $n$ . For each positive integer $n > 1$ , the number of fixed points and the in-degree of the elements $\bar{1}$ and $\bar{0}$ in $Γ (n)$ are found. Moreover, complete characterizations in terms of $n$ are given in which $Γ_{2} (n)$ is semiregular, where $Γ_{2} (n)$ is induced by all the zero-divisors of $ℤ_{n} [i]$ .

Displaying similar documents to “Structure of cubic mapping graphs for the ring of Gaussian integers modulo n ”

Isomorphic digraphs from powers modulo p

Characterization of power digraphs modulo n

The cubic mapping graph for the ring of Gaussian integers modulo n

Displaying similar documents to “Structure of cubic mapping graphs for the ring of Gaussian integers modulo $n$ ”

Isomorphic digraphs from powers modulo $p$

Characterization of power digraphs modulo $n$

The cubic mapping graph for the ring of Gaussian integers modulo $n$