The genus two class of graphs arising from rings

Asir T.

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The genus two class of graphs arising from rings

机译：来自戒指产生的两类图

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Given a commutative ring R with identity 1, its Jacobson graph J(R) is defined to be the graph in which the vertex set is RJ(R), and two distinct vertices x and y are adjacent if and only if 1 - xy is not an element of U(R). Here J(R) denotes the Jacobson radical of R and U(R) is the set of unit elements in R. This paper investigates the genus properties of Jacobson graph. In particular, we determine all isomorphism classes of commutative rings whose Jacobson graph has genus two.

机译：给定具有身份1的换向Ring R，其雅各逊图J（R）被定义为顶点组是R J（R）的图形，并且只有1 - XY不是U（R）的一个元素。这里j（r）表示R和U（R）的雅各逊激进族是R中的一组单元元素。本文研究了雅各的雅各逊图的属性。特别是，我们确定所有同义的换向环的换戒指，其雅各逊图具有两种。

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来源
《Journal of algebra and its applications》 |2018年第10期|共11页
作者
Asir T.;
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作者单位

Madurai Kamaraj Univ Dept Math DDE Madurai 625021 Tamil Nadu India;

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原文格式 PDF
正文语种 eng
中图分类代数、数论、组合理论;
关键词
Jacobson radical; Jacobson graph of a ring; genus of a graph;

机译：雅各逊激进的;雅各逊图的环;图的属;

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The genus two class of graphs arising from rings

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