论有限交换环的零因子图的顶点连通性

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Algebraic Combinatorics Pub Date : 2024-04-17 DOI:10.1007/s10801-024-01314-1

Sriparna Chattopadhyay, Kamal Lochan Patra, Binod Kumar Sahoo

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引用次数: 0

摘要

设 R 是具有同一性的有限交换环。我们将研究 R 的零分维图的结构，然后确定其顶点连通性，前提是：(i) R 是局部主理想环；(ii) R 是局部主理想环的有限直积：(i) R 是局部主理想环，以及 (ii) R 是局部主理想环的有限直积。对于这样的环 R，我们还确定了 R 的零因子图的最小度顶点和最小切集的特征。

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On vertex connectivity of zero-divisor graphs of finite commutative rings

Let R be a finite commutative ring with identity. We study the structure of the zero-divisor graph of R and then determine its vertex connectivity when: (i) R is a local principal ideal ring, and (ii) R is a finite direct product of local principal ideal rings. For such rings R, we also characterize the vertices of minimum degree and the minimum cut-sets of the zero-divisor graph of R.

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来源期刊

Journal of Algebraic Combinatorics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.