Some results on a supergraph of the sum annihilating ideal graph of a commutative ring

被引:0
|
作者
Visweswaran, S. [1 ]
机构
[1] Saurashtra Univ, Dept Math, Rajkot 360005, India
关键词
Annihilating ideal graph; sum annihilating ideal graph; maximal N-prime of (0); connectedness; diameter; radius;
D O I
10.1142/S1793830923500878
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The rings considered in this paper are commutative with identity which are not integral domains. Let R be a ring. An ideal I of R is said to be an annihilating ideal if there exists r is an element of R\{0} such that Ir = (0). Let A(R) denote the set of all annihilating ideals of R and we denote A(R)\{(0)} by A(R)*. With R, in this paper, we associate an undirected graph denoted by S Omega(R) whose vertex set is A(R)* and two distinct vertices I, J are adjacent in this graph if and only if either IJ = (0) or I + J is an element of A(R). The aim of this paper is to study the interplay between some graph properties of S Omega(R) and the algebraic properties of R and to compare some graph properties of S Omega(R) with the corresponding graph properties of the annihilating ideal graph of R and the sum annihilating ideal graph of R.
引用
收藏
页数:34
相关论文
共 50 条
  • [41] On the Comaximal Graph of a Commutative Ring
    Samei, Karim
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2014, 57 (02): : 413 - 423
  • [42] On the annihilator-ideal graph of commutative rings
    Sepideh Salehifar
    Kazem Khashyarmanesh
    Mojgan Afkhami
    Ricerche di Matematica, 2017, 66 : 431 - 447
  • [43] On the annihilator-ideal graph of commutative rings
    Salehifar, Sepideh
    Khashyarmanesh, Kazem
    Afkhami, Mojgan
    RICERCHE DI MATEMATICA, 2017, 66 (02) : 431 - 447
  • [44] THE GENERALIZED TOTAL GRAPH OF A COMMUTATIVE RING
    Anderson, David F.
    Badawi, Ayman
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2013, 12 (05)
  • [45] When a line graph associated to annihilating-ideal graph of a lattice is planar or projective
    Atossa Parsapour
    Khadijeh Ahmad Javaheri
    Czechoslovak Mathematical Journal, 2018, 68 : 19 - 34
  • [46] On the Structure of Nil Graph of a Commutative Ring
    Patra, Kuntala
    Begum, Shazida
    MATEMATIKA, 2015, 31 (01) : 37 - 45
  • [47] THE TRIPLE ZERO GRAPH OF A COMMUTATIVE RING
    Yetkin Celikel, Ece
    COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2021, 70 (02): : 653 - 663
  • [48] A new graph associated to a commutative ring
    Alilou, A.
    Amjadi, J.
    Sheikholeslami, S. M.
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2016, 8 (02)
  • [49] The Weakly Nilpotent Graph of a Commutative Ring
    Khojasteh, Soheila
    Nikmehr, Mohammad Javad
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2017, 60 (02): : 319 - 328
  • [50] When a line graph associated to annihilating-ideal graph of a lattice is planar or projective
    Parsapour, Atossa
    Javaheri, Khadijeh Ahmad
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2018, 68 (01) : 19 - 34