ON METRIC DIMENSION AND RESOLVING-DOMINATION NUMBER OF ZERO-DIVISOR GRAPHS OF DIRECT PRODUCT OF FINITE FIELDS

The main objective of this paper is to calculate the metric dimension and resolving-domination number zero-divisor graphs direct product finite fields. Let $F_1, \ldots, F_n(n \geqslant 2)$ be We consider graph $\Gamma(R)$ ring $R=F_1 \times \cdots F_n$ $(n determine $\beta(\Gamma(R))$ $\gamma_r(\Gamma(R))$ If order each field two, then we prove that $\beta(\Gamma(R)) \leqslant n-1$ $\gamma_r(\Gamma(R))=n$. at least 3 , are both equal $|V(\Gamma(R))|-\left(2^n-2\right)$. Received: February 19, 2023 Revised: July 1, Accepted: 4,