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 ≡ 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 , ⋯ , n - 1 } as the set of vertices and E = { ( a , b ) : a k ≡ 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 1 ¯ and 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 ] .