In this study, we define a zero-divisor graph of a commutative ring with a new sign function. The basic structure and distances in signed zero-divisor graphs are also discussed. This study aims to provide a deeper understanding of signed zero-divisor graphs by examining their properties such as balancing and distance compatibility. Then, we define the strong metric dimension in distance compatible signed graphs, and we evaluate the strong metric dimension of signed zero-divisor graphs of commutative rings.
Akhila et al. (Tue,) studied this question.