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

Yangjiang Wei; Jizhu Nan; Gaohua Tang

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 4, page 1023-1036
  • ISSN: 0011-4642

Abstract

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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 ] .

How to cite

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Wei, Yangjiang, Nan, Jizhu, and Tang, Gaohua. "The cubic mapping graph for the ring of Gaussian integers modulo $n$." Czechoslovak Mathematical Journal 61.4 (2011): 1023-1036. <http://eudml.org/doc/196934>.

@article{Wei2011,
abstract = {The article studies the cubic mapping graph $\Gamma (n)$ of $\mathbb \{Z\}_n[\{\rm i\}]$, 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 $\Gamma (n)$ are found. Moreover, complete characterizations in terms of $n$ are given in which $\Gamma _\{2\}(n)$ is semiregular, where $\Gamma _\{2\}(n)$ is induced by all the zero-divisors of $\mathbb \{Z\}_n[\{\rm i\}]$.},
author = {Wei, Yangjiang, Nan, Jizhu, Tang, Gaohua},
journal = {Czechoslovak Mathematical Journal},
keywords = {Gaussian integers modulo $n$; cubic mapping graph; fixed point; semiregularity; Gaussian integers modulo ; cubic mapping graph; fixed point; semiregularity},
language = {eng},
number = {4},
pages = {1023-1036},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The cubic mapping graph for the ring of Gaussian integers modulo $n$},
url = {http://eudml.org/doc/196934},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Wei, Yangjiang
AU - Nan, Jizhu
AU - Tang, Gaohua
TI - The cubic mapping graph for the ring of Gaussian integers modulo $n$
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 1023
EP - 1036
AB - The article studies the cubic mapping graph $\Gamma (n)$ of $\mathbb {Z}_n[{\rm i}]$, 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 $\Gamma (n)$ are found. Moreover, complete characterizations in terms of $n$ are given in which $\Gamma _{2}(n)$ is semiregular, where $\Gamma _{2}(n)$ is induced by all the zero-divisors of $\mathbb {Z}_n[{\rm i}]$.
LA - eng
KW - Gaussian integers modulo $n$; cubic mapping graph; fixed point; semiregularity; Gaussian integers modulo ; cubic mapping graph; fixed point; semiregularity
UR - http://eudml.org/doc/196934
ER -

References

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  7. Su, H. D., Tang, G. H., The prime spectrum and zero-divisors of ℤ n [ i ] , J. Guangxi Teach. Edu. Univ. 23 (2006), 1-4. (2006) 
  8. Tang, G. H., Su, H. D., Yi, Z., The structure of the unit group of ℤ n [ i ] , J. Guangxi Norm. Univ., Nat. Sci. 28 (2010), 38-41. (2010) 
  9. Wei, Y. J., Nan, J. Z., Tang, G. H., Su, H. D., The cubic mapping graphs of the residue classes of integers, Ars Combin. 97 (2010), 101-110. (2010) MR2732885

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