Southeast Asian Bulletin of Mathematics, Volume (39), No (1), Year (2015-2) , Pages (13-34)

Title : ( A dual of regular digraph of commutative rings )

Authors: M. Afkhami , M. Karimi , Kazem Khashyarmanesh ,

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Let R be a Noetherian commutative ring. The regular digraph of ideals of R introduced in [10] which denoted by −−→ Γreg(R). The vertex set of −−→ Γreg(R) is set of nontrivial ideals of R and I −→ J is an arc in Γ(R) if and only if I ⊈ Z(J). In this paper we will introduce a dual of −−→ Γreg(R) and denote it by Γ∗(R). The vertex set of Γ∗(R) is set of nontrivial ideals of R and I −→ J is an arc in Γ∗(R) if and only if there exists an element x in I such that the R−module homomorphism fx : J −→ J is an epimorphism by the rule fx(y) = yx. We investigate the interplay between Γ∗(R) and ring-theoretic properties of R and graph-theoretic properties of Γ∗(R). Also we study the relation between two graphs Γ(R) and Γ∗(R). In particular we will show that the value of !(Γreg(R)) in [10] is not correct, and we will compute the correct value of w(Γreg(R)).

Keywords

Regular digraph; Connectedness; Girth; Clique number; Chromatic
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@article{paperid:1054715,
author = {M. Afkhami and M. Karimi and Khashyarmanesh, Kazem},
title = {A dual of regular digraph of commutative rings},
journal = {Southeast Asian Bulletin of Mathematics},
year = {2015},
volume = {39},
number = {1},
month = {February},
issn = {0129-2021},
pages = {13--34},
numpages = {21},
keywords = {Regular digraph; Connectedness; Girth; Clique number; Chromatic number.},
}

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%0 Journal Article
%T A dual of regular digraph of commutative rings
%A M. Afkhami
%A M. Karimi
%A Khashyarmanesh, Kazem
%J Southeast Asian Bulletin of Mathematics
%@ 0129-2021
%D 2015

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