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

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Abstract

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 \(\overline 1 \) and \(\overline 0 \) in Γ(n) are found. Moreover, complete characterizations in terms of n are given in which Γ2(n) is semiregular, where Γ2(n) is induced by all the zero-divisors of ℤ n [i].

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P.R. China

    Yangjiang Wei & Jizhu Nan

  2. School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, 530023, P.R. China

    Gaohua Tang

Authors
  1. Yangjiang Wei
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  2. Jizhu Nan
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  3. Gaohua Tang
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Corresponding author

Correspondence to Yangjiang Wei.

Additional information

This research was supported by the National Natural Science Foundation of China (11161006, 11171142), the Guangxi natural Science Foundation (2011GXNSFA018139), the Guangxi New Century 1000Talents Project and the Scientific Research Foundation of Guangxi Educational Committee (201012MS140).

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Wei, Y., Nan, J. & Tang, G. The cubic mapping graph for the ring of Gaussian integers modulo n . Czech Math J 61, 1023–1036 (2011). https://doi.org/10.1007/s10587-011-0045-7

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  • DOI: https://doi.org/10.1007/s10587-011-0045-7

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