Metric and Strong Metric Dimension in Cozero-Divisor Graphs

Let R be a commutative ring with non-zero identity and W ∗ ( R ) be the set of all non-zero and non-unit elements of R . The cozero-divisor graph of R , denoted by Γ ′ ( R ) , is a graph with the vertex set W ∗ ( R ) and two distinct vertices a and b are adjacent if and only if a ∉ R b and b ∉ R a ....

Full description

Saved in:
Bibliographic Details
Published in:Mediterranean journal of mathematics 2021-06, Vol.18 (3), Article 112
Main Authors: Nikandish, R., Nikmehr, M. J., Bakhtyiari, M.
Format: Article
Language:English
Subjects:
Apexes
Commutativity
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Rings (mathematics)
Vertex sets
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let R be a commutative ring with non-zero identity and W ∗ ( R ) be the set of all non-zero and non-unit elements of R . The cozero-divisor graph of R , denoted by Γ ′ ( R ) , is a graph with the vertex set W ∗ ( R ) and two distinct vertices a and b are adjacent if and only if a ∉ R b and b ∉ R a . In this paper, the metric dimension and strong metric dimension of Γ ′ ( R ) are investigated. We compute the exact values of strong metric and metric dimension in cozero-divisor graphs of reduced rings. Moreover, the metric dimension in cozero-divisor graphs of non-reduced rings is discussed.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-021-01772-y