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

نویسندگان
P V, Shamsudheen ID 1
A T, Shahida ID 2

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

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

doi
10.22075/ijnaa.2022.22867.3474
چکیده

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.

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