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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. |
| 关键词: 模n高斯整数环 半正则性 高度 |
| DOI： |
| 分类号:O153.3;O156.1;O157.5 |
| 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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| THE SQUARE MAPPING GRAPHS OF THE RING Zn[i] |
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WEI Yang-jiang,TANG Gao-hua
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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. |
| Key words: Gaussian integers modulo n semiregularity height |
