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.
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页数：16
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