International Journal of Nonlinear Analysis and Applications

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

Document Type : Research Paper

Authors

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

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 11
November 2023
Pages 365-373
  • Receive Date: 04 May 2022
  • Revise Date: 15 June 2022
  • Accept Date: 07 July 2022