广西师范大学学报（自然科学版）2016，Vol.34Issue(3)：53-61,9.DOI:10.16088/j.issn.1001-6600.2016.03.008
模n高斯整数环的商环的立方映射图
Cubic Mapping Graphs on the Quotient Rings of the Gaussian Integer Rings of Modulo n
摘要
Abstract
Let Z[i]be the ring of Gaussian integers,γ∈Z[i].Let ‹γ›denote the ideal of Z[i]generated byγ.The cubic mapping graph G(γ)over the quotient ring Z[i]/‹γ›is a digraph,where the vertices of G(γ)are the elements of Z[i]/‹γ›,and there is a directed edge fromαtoβifβ=α3 .In this paper,the structure of G(γ)is investigated.The numbers of the fixed points and the in-degree of the vertices 0 and 1 are obtained.Moreover,the semiregularity of the graph G(γ)is characterized.Finally,the height in G (γ)of an arbitrary zero-divisor is determined.关键词
高斯整数环/立方映射图/入度/圈/半正则性Key words
Gaussian integers/cubic mapping graph/in-degree/cycles/semiregular分类
数理科学引用本文复制引用
韦扬江,梁艺耀,唐高华,苏磊磊,陈蔚凝..模n高斯整数环的商环的立方映射图[J].广西师范大学学报（自然科学版）,2016,34(3):53-61,9.基金项目
国家自然科学基金资助项目(11461010,11661014) （11461010,11661014）
广西自然科学基金资助项目(2014GXNSFAA118005) （2014GXNSFAA118005）
广西科学研究与技术开发项目(桂科合1599005-2-13) （桂科合1599005-2-13）
广西高校科学技术研究项目(KY2015ZD075) （KY2015ZD075）
