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

Yangjiang Wei, Jizhu Nan, Gaohua Tang (2011)

Czechoslovak Mathematical Journal

The article studies the cubic mapping graph Γ ( n ) of 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 n [ i ] .

The fundamental constituents of iteration digraphs of finite commutative rings

Jizhu Nan, Yangjiang Wei, Gaohua Tang (2014)

Czechoslovak Mathematical Journal

For a finite commutative ring R and a positive integer k 2 , we construct an iteration digraph G ( R , k ) whose vertex set is R and for which there is a directed edge from a R to b R if b = a k . Let R = R 1 ... R s , where s > 1 and R i is a finite commutative local ring for i { 1 , ... , s } . Let N be a subset of { R 1 , , R s } (it is possible that N is the empty set ). We define the fundamental constituents G N * ( R , k ) of G ( R , k ) induced by the vertices which are of the form { ( a 1 , , a s ) R : a i D ( R i ) if R i N , otherwise a i U ( R i ) , i = 1 , ... , s } , where U ( R ) denotes the unit group of R and D ( R ) denotes the zero-divisor set of R . We investigate...

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