A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10256443" target="_blank" >RIV/61989100:27740/24:10256443 - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S2405844024070208?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2405844024070208?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.heliyon.2024.e30989" target="_blank" >10.1016/j.heliyon.2024.e30989</a>

Result language

angličtina

Original language name

A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs

Original language description

This article investigates the concept of dominant metric dimensions in zero divisor graphs (ZDgraphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if their product results in zero (x . y = 0). The set of zero divisors in ring R is referred to as L(R). To analyze various algebraic properties of R, a graph known as the zero-divisor graph is constructed using L(R). This manuscript establishes specific general bounds for the dominant metric dimension (Ddim) concerning the ZD-graph of R. To achieve this objective, we examine the zero divisor graphs for specific rings, such as the ring of Gaussian integers modulo m, denoted as Zm[i], the ring of integers modulo n, denoted as Zn, and some quotient polynomial rings. Our research unveils new insights into the structural similarities and differences among commutative rings sharing identical metric dimensions and dominant metric dimensions. Additionally, we present a general result outlining bounds for the dominant metric dimension expressed in terms of the maximum degree, girth, clique number, and diameter of the associated ZD-graphs. Through this exploration, we aim to provide a comprehensive framework for analyzing commutative rings and their associated zero divisor graphs, thereby advancing both theoretical knowledge and practical applications in diverse domains.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10700 - Other natural sciences

Project

—

Continuities

O - Projekt operacniho programu

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Heliyon

ISSN

2405-8440

e-ISSN

2405-8440

Volume of the periodical

10

Issue of the periodical within the volume

10

Country of publishing house

GB - UNITED KINGDOM

Number of pages

8

Pages from-to

—

UT code for WoS article

001298423700001

EID of the result in the Scopus database

2-s2.0-85193532089