Z_n[i]的平方映射图（英文）  

THE SQUARE MAPPING GRAPHS OF THE RING Z_n[i]

作　　者：韦扬江[1] 唐高华[1] 

机构地区：[1]广西师范学院数学与统计学院,广西南宁530023

出　　处：《数学杂志》2016年第4期676-682,共7页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China(11161006,11461010);the Guangxi Natural Science Foundation(2014GXNSFAA118005)

摘　　要：本文研究了模n高斯整数环Z_n[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.In this paper,we investigate some properties of the square mapping graphs Γ（n）of Z_n[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 Γ_2（n） is semiregular,where Γ_2（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 Zngiven by Somer.

关 键 词：模n高斯整数环 半正则性 高度 

分 类 号：O153.3[理学—数学] O156.1[理学—基础数学]