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

[21] More on the annihilator-ideal graph of a commutative ring
Nikmehr, M. J.
Hosseini, S. M.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2019, 18 (08)
[22] The annihilator-inclusion ideal graph of a commutative ring
Amjadi, Jafar
Khoeilar, Rana
Alilou, Abbas
COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 2021, 6 (02) : 231 - 248
[23] More on the annihilator-ideal graph of a commutative ring
Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
arXiv, 1600,
[24] On the Genus of the Annihilator-Ideal Graph of Commutative Ring
Krishnan, Selvakumar
Shunmugaiah, Karthik
MATHEMATICS AND COMPUTING, ICMC 2022, 2022, 415 : 165 - 174
[25] A Note on Comaximal Graph of Non-commutative Rings
Saieed Akbari
Mohammad Habibi
Ali Majidinya
Raoofe Manaviyat
Algebras and Representation Theory, 2013, 16 : 303 - 307
[26] Comaximal graph of amalgamated algebras along an ideal
Shoar, Hanieh
Salimi, Maryam
Tehranian, Abolfazl
Rasouli, Hamid
Tavasoli, Elham
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2023, 22 (01)
[27] Some Results on the Comaximal Colon Ideal Graph
Rajaee, S.
Abbasi, A.
JOURNAL OF MATHEMATICAL EXTENSION, 2022, 16 (11)
[28] Some results on the complement of the comaximal ideal graphs of commutative rings
Visweswaran, S.
Parejiya, Jaydeep
RICERCHE DI MATEMATICA, 2018, 67 (02) : 709 - 728
[29] Some results on the complement of the comaximal ideal graphs of commutative rings
S. Visweswaran
Jaydeep Parejiya
Ricerche di Matematica, 2018, 67 : 709 - 728
[30] Some further results on the annihilator ideal graph of a commutative ring
1600, Politechnica University of Bucharest (79):

← 1 2 3 4 5 →