# The regular digraph of ideals of a commutative ring

@article{Nikmehr2012TheRD, title={The regular digraph of ideals of a commutative ring}, author={Mohammad Javad Nikmehr and Farzad Shaveisi}, journal={Acta Mathematica Hungarica}, year={2012}, volume={134}, pages={516-528} }

AbstractLet R be a commutative ring and Max (R) be the set of maximal ideals of R. The regular digraph of ideals of R, denoted by
$\overrightarrow{\Gamma_{\mathrm{reg}}}(R)$
, is a digraph whose vertex set is the set of all non-trivial ideals of R and for every two distinct vertices I and J, there is an arc from I to J whenever I contains a J-regular element. The undirected regular (simple) graph of ideals of R, denoted by Γreg(R), has an edge joining I and J whenever either I contains a J…

## 20 Citations

On the girth of regular digraph of ideals of an Artinian ring

- MathematicsAKCE Int. J. Graphs Comb.
- 2015

ON THE REGULAR DIGRAPH OF IDEALS OF COMMUTATIVE RINGS

- MathematicsBulletin of the Australian Mathematical Society
- 2012

Abstract Let $R$ be a commutative ring. The regular digraph of ideals of $R$, denoted by $\Gamma (R)$, is a digraph whose vertex set is the set of all nontrivial ideals of $R$ and, for every two…

Cayley graphs of ideals in a commutative ring

- Mathematics
- 2014

Let R be a commutative ring. We associate a digraph to the ideals of R whose vertex set is the set of all nontrivial ideals of R and, for every two distinct vertices I and J , there is an arc from I…

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- Mathematics
- 2018

Let R be a commutative ring with an identity. Let Spec(R) be the set of all prime ideals of R and Max(R) be the set of all maximal ideals of R. Let S Max(R). We de ne an S-proper ideal sum graph on…

The M-Regular Graph of a Commutative Ring

- Mathematics
- 2013

Abstract Let R be a commutative ring and M be an R-module, and let Z(M) be the set of all zero-divisors on M. In 2008, D. F. Anderson and A. Badawi introduced the regular graph of R. In this paper,…

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- Mathematics
- 2019

Let $$(P,\le )$$(P,≤) be a partially ordered set with a least element 0. The regular digraph of ideals of P, denoted by $$\overrightarrow{\Gamma }(P)$$Γ→(P), is a digraph whose vertex-set is the set…

The Nil-Graph of Ideals of a Commutative Ring

- Mathematics
- 2016

Let R be a commutative ring with identity and $$\mathrm{Nil}(R)$$Nil(R) be the set of nilpotent elements of R. The nil-graph of ideals of R is defined as the graph $${\mathbb {AG}}_N(R)$$AGN(R) whose…

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- Mathematics
- 2015

The regular graph of ideals of the commutative ring $R$, denoted by $\Gamma_{reg}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$…

The Center and Radius of the Regular Graph of Ideals

- Mathematics
- 2015

The regular graph of ideals of the commutative ring $R$, denoted by ${\Gamma_{reg}}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$…

The central vertices and radius of the regular graph of ideals

- Mathematics
- 2017

The regular graph of ideals of the commutative ring $R$, denoted by ${Gamma_{reg}}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and…

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