Document Type : Research Paper

Authors

• Shamsudheen P V
• Shahida A T

Department of Mathematics, MES Mampad College Malappuram-676542, India

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