On the comaximal ideal graph of a commutative ring

被引：8

作者：

Azadi, Mehrdad ^{[1
]}

Jafari, Zeinab ^{[1
]}

Eslahchi, Changiz ^{[2
]}

机构：

[1] Islamic Azad Univ, Cent Tehran Branch, Dept Math, Tehran, Iran

[2] Shahid Beheshti Univ, Dept Comp Sci, Tehran, Iran

来源：

TURKISH JOURNAL OF MATHEMATICS | 2016年 / 40卷 / 04期

关键词：

Chromatic number; clique number; planar graph; perfect graph;

D O I：

10.3906/mat-1505-23

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a commutative ring with identity. We use Gamma(R) to denote the comaximal ideal graph. The vertices of Gamma(R) are proper ideals of R that are not contained in the Jacobson radical of R, and two vertices I and J are adjacent if and only if I + J = R. In this paper we show some properties of this graph together with the planarity and perfection of Gamma(R).

引用

页码：905 / 913

页数：9

共 50 条

[1] SOME RESULTS ON THE COMAXIMAL IDEAL GRAPH OF A COMMUTATIVE RING
Dorbidi, Hamid Reza
Manaviyat, Raoufeh
TRANSACTIONS ON COMBINATORICS, 2016, 5 (04) : 9 - 20
[2] On the Comaximal Graph of a Commutative Ring
Samei, Karim
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2014, 57 (02): : 413 - 423
[3] A note on comaximal ideal graph of commutative rings
Kavitha, S.
Kala, R.
AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 2020, 17 (01) : 453 - 460
[4] The automorphism group of the comaximal graph of a commutative ring
Khashyarmanesh, Kazem
Mehdi-Nezhad, Elham
Rahimi, Amir M.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024,
[5] Some properties of generalized comaximal graph of commutative ring
B. Biswas
S. Kar
Soft Computing, 2024, 28 : 3783 - 3791
[6] Some properties of generalized comaximal graph of commutative ring
Biswas, B.
Kar, S.
SOFT COMPUTING, 2024, 28 (05) : 3783 - 3791
[7] Cut vertices in comaximal graph of a commutative Artinian ring
Kyuoomars Esmaili
Karim Samei
Indian Journal of Pure and Applied Mathematics, 2021, 52 : 340 - 343
[8] Cut vertices in comaximal graph of a commutative Artinian ring
Esmaili, Kyuoomars
Samei, Karim
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2021, 52 (02): : 340 - 343
[9] Comaximal graph of commutative rings
Maimani, Hamid Reza
Safimi, Maryam
Sattari, Asiyeh
Yassemi, Siamak
JOURNAL OF ALGEBRA, 2008, 319 (04) : 1801 - 1808
[10] Some properties of comaximal right ideal graph of a ring
Shen, Shouqiang
Liu, Weijun
Feng, Lihua
APPLIED MATHEMATICS AND COMPUTATION, 2018, 333 : 225 - 230

← 1 2 3 4 5 →