Ricerche di Matematica, Volume (66), No (2), Year (2017-10) , Pages (431-447)

Title : ( On the annihilator-ideal graph of commutative rings )

Authors: sepide salehifar , Kazem Khashyarmanesh , M. Afkhami ,

Access to full-text not allowed by authors

Citation: BibTeX | EndNote


Let R be a commutative ring with nonzero identity. We denote by AG(R) the annihilator graph of R,whose vertex set consists of the set of nonzero zero-divisors of R, and two distint vertices x and y are adjacent if and only if ann(x) ∪ ann(y)\not equal ann(xy), where for t ∈ R, we set ann(t) := {r ∈ R | rt = 0}. In this paper, we define the annihiator-ideal graph of R, which is denoted by AI (R), as an undirected graph with vertex set A_*(R), and two distinct vertices I and J are adjacent if and only if ann(I ) ∪ ann(J ) \not= ann(I J). We study some basic properties of AI (R) such as connectivity, diameter and girth. Also we investigate the situations under which the graphs AG(R) and AI (R) are coincide. Moreover, we examin the planarity of the graph AI (R).


, Annihilating-ideal graph , Bipartite graph , Planar graph
برای دانلود از شناسه و رمز عبور پرتال پویا استفاده کنید.

author = {Salehifar, Sepide and Khashyarmanesh, Kazem and M. Afkhami},
title = {On the annihilator-ideal graph of commutative rings},
journal = {Ricerche di Matematica},
year = {2017},
volume = {66},
number = {2},
month = {October},
issn = {0035-5038},
pages = {431--447},
numpages = {16},
keywords = {Annihilating-ideal graph ;Bipartite graph ;Planar graph},


%0 Journal Article
%T On the annihilator-ideal graph of commutative rings
%A Salehifar, Sepide
%A Khashyarmanesh, Kazem
%A M. Afkhami
%J Ricerche di Matematica
%@ 0035-5038
%D 2017