DOMINATION NUMBER IN THE ANNIHILATING-IDEAL GRAPHS OF COMMUTATIVE RINGS

被引：10

作者：

Nikandish, Reza ^{[1
]}

Maimani, Hamid Reza ^{[2
,3
]}

Kiani, Sima ^{[4
]}

机构：

[1] Jundi Shapur Univ Technol, Dept Math, Dezful, Iran

[2] Shahid Rajaee Teacher Training Univ, Dept Basic Sci, Math Sect, Tehran, Iran

[3] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

[4] Islamic Azad Univ, Sci & Res Branch, Dept Math, Tehran, Iran

来源：

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD | 2015年 / 97卷 / 111期

关键词：

annihilating-ideal graph; zero-divisor graph; domination number; minimal prime ideal;

D O I：

10.2298/PIM140222001N

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R be a commutative ring with identity and A(R) be the set of ideals with nonzero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)* = A(R) \ {0} and two distinct vertices I and J are adjacent if and only if IJ = 0. In this paper, we study the domination number of AG(R) and some connections between the domination numbers of annihilating-ideal graphs and zero-divisor graphs are given.

引用

页码：225 / 231

页数：7

共 50 条

[31] On Domination in Graphs from Commutative Rings: A Survey
Chelvam, T. Tamizh
Asir, T.
Selvakumar, K.
ALGEBRA AND ITS APPLICATIONS, ICAA 2014, 2016, 174 : 363 - 379
[32] The Annihilating-Ideal Graph of an Idealization
Ahrari, M.
Sabet, Sh. A. Safari
Amini, B.
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2017, 41 (A1): : 165 - 168
[33] The Annihilating-Ideal Graph of an Idealization
M. Ahrari
Sh. A. Safari Sabet
B. Amini
Iranian Journal of Science and Technology, Transactions A: Science, 2017, 41 : 165 - 168
[34] The annihilating-ideal graph of a lattice
Afkhami, Mojgan
Bahrami, Solmaz
Khashyarmanesh, Kazem
Shahsavar, Faeze
GEORGIAN MATHEMATICAL JOURNAL, 2016, 23 (01) : 1 - 7
[35] SOME RESULTS ON ANNIHILATING IDEAL GRAPH OF COMMUTATIVE RINGS
Tayade, P. N.
Surwade, K.
Deore, R. P.
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2018, 40 (04): : 501 - 514
[36] On Annihilating Graphs Associated with Modules over Commutative Rings
Raja, Rameez
Pirzada, Shariefuddin
ALGEBRA COLLOQUIUM, 2022, 29 (02) : 281 - 296
[37] Domination number of graphs associated with rings
Hashemi, Ebrahim
Abdi, Mona
Alhevaz, Abdollah
Su, Huadong
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2020, 19 (01)
[38] Some results on a spanning subgraph of the complement of the annihilating-ideal graph of a commutative reduced ring
Visweswaran, S.
Parmar, Anirudhdha
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2019, 11 (01)
[39] LINE GRAPHS ASSOCIATED TO ANNIHILATING-IDEAL GRAPH ATTACHED TO LATTICES OF GENUS ONE
Parsapour, Atossa
Javaheri, Khadijeh Ahmad
TRANSACTIONS ON COMBINATORICS, 2023, 12 (04) : 175 - 190
[40] THE ANNIHILATING-IDEAL GRAPH OF Zn IS WEAKLY PERFECT
Nikandish, Reza
Maimani, Hamid Reza
Izanloo, Hasan
CONTRIBUTIONS TO DISCRETE MATHEMATICS, 2016, 11 (01) : 16 - 21

← 1 2 3 4 5 →