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The article studies the cubic mapping graph of , the ring of Gaussian integers modulo . For each positive integer , the number of fixed points and the in-degree of the elements and in are found. Moreover, complete characterizations in terms of are given in which is semiregular, where is induced by all the zero-divisors of .
For a finite commutative ring and a positive integer , we construct an iteration digraph whose vertex set is and for which there is a directed edge from to if . Let , where and is a finite commutative local ring for . Let be a subset of (it is possible that is the empty set ). We define the fundamental constituents of induced by the vertices which are of the form if , otherwise where U denotes the unit group of and D denotes the zero-divisor set of . We investigate...
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