On the Genus of Strong Annihilating-ideal Graph of Commutative Rings

被引：0

作者：

Nazim, Mohd ^{[1
]}

Rehman, Nadeem Ur ^{[1
]}

Selvakumar, K. ^{[2
]}

机构：

[1] Aligarh Muslim Univ, Dept Math, Aligarh 202002, India

[2] Manonmaniam Sundaranar Univ, Dept Math, Tirunelveli, Tamil Nadu, India

来源：

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2023年 / 16卷 / 09期

关键词：

Zero-divisor graph; annihilating-ideal graph; strong annihilating-ideal graph; planar graph; genus of a graph; ZERO-DIVISOR GRAPH;

D O I：

10.1142/S1793557123501668

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a commutative ring with unity and A(R) be the set of annihilating-ideals of R. The strong annihilating-ideal graph of R, denoted by SAG(R), is an undirected graph with vertex set A(R)* and two vertices I-1 and I-2 are adjacent if and only if I-1 boolean AND Ann(I-2) not equal (0) and I-2 boolean AND Ann(I-1) not equal (0). In this paper, first we characterize commutative Artinian rings whose strong annihilating-ideal graph is isomorphic to some well-known graphs and then we classify commutative Artinian rings whose strong annihilating-ideal graph is planar, toroidal or projective.

引用

页数：16

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