On the metric dimension of a total graph of non-zero annihilating ideals-Reference-Cited by-同舟云学术

On the metric dimension of a total graph of non-zero annihilating ideals

Published:2020-12-01 Issue:3 Volume:28 Page:5-14
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Abachi Nazi¹,Sahebi Shervin²

Affiliation:

1. Department of Mathematics , Central Tehran Branch , Islamic Azad University Tehran , Iran , P. O. Box 14168-94351 .

2. Department of Mathematics , Central Tehran Branch , Islamic Azad University Tehran , Iran , P. O. Box 14168-94351.

Abstract

Abstract Let R be a commutative ring with identity which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r ∈ R − {0} such that Ir = (0). Visweswaran and H. D. Patel associated a graph with the set of all non-zero annihilating ideals of R, denoted by Ω(R) as the graph with the vertex-set A(R)*, the set of all non-zero annihilating ideals of R and two distinct vertices I, J are joined if and only if I +J is also an annihilating ideal of R. In this paper, we study the metric dimension of Ω(R) and provide metric dimension formulas for Ω(R).

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2020-0031

Reference15 articles.

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