| Zn[i] 的平方映射图 |
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| 引用本文： | 韦扬江,唐高华. Zn[i] 的平方映射图[J]. 数学杂志, 2016, 36(4): 676-682 |
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| 作者姓名： | 韦扬江 唐高华 |
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| 作者单位： | 广西师范学院数学与统计学院, 广西 南宁 530023,广西师范学院数学与统计学院, 广西 南宁 530023 |
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| 基金项目： | Supported by the National Natural Science Foundation of China (11161006; 11461010); the Guangxi Natural Science Foundation (2014GXNSFAA118005). |
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| 摘 要： | 本文研究了模n 高斯整数环Zn[i] 的平方映射图Γ(n). 利用数论、图论与群论等方法, 获得了Γ(n) 中顶点0 及1 的入度, 并研究了Γ(n) 的零因子子图的半正则性. 同时, 获得了Γ(n) 中顶点的高度公式.推广了Somer 等人给出的模n 剩余类环平方映射图的相关结论.
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| 关 键 词： | 模n高斯整数环 半正则性 高度 |
| 收稿时间： | 2014-08-25 |
| 修稿时间： | 2015-01-23 |
THE SQUARE MAPPING GRAPHS OF THE RING Zn[i] |
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| WEI Yang-jiang and TANG Gao-hua. THE SQUARE MAPPING GRAPHS OF THE RING Zn[i][J]. Journal of Mathematics, 2016, 36(4): 676-682 |
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| Authors: | WEI Yang-jiang and TANG Gao-hua |
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| Affiliation: | School of Mathematical Sciences, Guangxi Teachers Education University, Nanning 530023, China and School of Mathematical Sciences, Guangxi Teachers Education University, Nanning 530023, China |
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| Abstract: | In this paper, we investigate some properties of the square mapping graphs Γ(n) of Zn[i], the ring of Gaussian integers modulo n. Using the method of number theory, graph theory and group theory, we obtain the in-degree of 0 and 1. Moreover, we give the complete characterizations in terms of n in which Γ2(n) is semiregular, where Γ2(n) is induced by all the zero-divisors of Zn[i]. The formulas on the heights of vertices in Γ(n) are also obtained. This paper extends results concerning the square mapping graphs of Zn given by Somer. |
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| Keywords: | Gaussian integers modulo n semiregularity height |
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