Metric dimension and neighbourhood resolving set for the zero divisor graphs of order at most 10 of a small finite commutative ring

Author(s):

Shamsudheen P V , Shahida A T *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
Let $R$ be a commutative ring and $\Gamma(R)$  be its zero-divisor graph. All the vertices of zero divisor graphs are the non-zero divisors of the commutative ring, with two distinct vertices joined by an edge in case their product in the commutative ring is zero. In this paper, we study the metric dimension and neighbourhood resoling set for the zero divisor graphs of order 3,4,5,6,7,8,9,10 of a small finite commutative ring with a unit.
Keywords:

Commutative ring , Zero divisor graph , Resolving set , Metric Dimension , Neighbourhood set

Language:
English
Published:
International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 11, Nov 2023
Pages:
365 to 373
https://www.magiran.com/p2665202