Note di Matematica, Volume (36), No (1), Year (2016-3) , Pages (1-10)

Title : ( The annihilator ideal graph of a commutative ring )

Authors: M. Afkhami , Seyede Nesa Hoseini , Kazem Khashyarmanesh ,

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Let R be a commutative ring with nonzero identity and I be a proper ideal of R. The annihilator graph of R with respect to I, which is denoted by AGI (R), is the undirected graph with vertex-set V(AGI (R)) ={x in R-I : xy in I for some y not in I} and two distinct vertices x and y are adjacent if and only if AI (xy) not= AI (x) UAI (y), where AI (x) = {r in R : rx in I}. In this paper, we study some basic properties of AGI(R), and we characterise when AGI (R) is planar, outerplanar or a ring graph. Also, we study the graph AGI(Zn), where Z-n is the ring of integers modulo n.

Keywords

, Zero-divisor graph, Annihilator graph, Girth, Planar graph, Outerplanar, Ring
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@article{paperid:1060929,
author = {M. Afkhami and Hoseini, Seyede Nesa and Khashyarmanesh, Kazem},
title = {The annihilator ideal graph of a commutative ring},
journal = {Note di Matematica},
year = {2016},
volume = {36},
number = {1},
month = {March},
issn = {1123-2536},
pages = {1--10},
numpages = {9},
keywords = {Zero-divisor graph; Annihilator graph; Girth; Planar graph; Outerplanar; Ring graph},
}

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%0 Journal Article
%T The annihilator ideal graph of a commutative ring
%A M. Afkhami
%A Hoseini, Seyede Nesa
%A Khashyarmanesh, Kazem
%J Note di Matematica
%@ 1123-2536
%D 2016

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