Optimizing SNARK networks via double metric dimension

Doubly resolving sets (DRSs) provide a promising approach for source detection. They consist of minimal subsets of nodes with the smallest cardinality, referred to as the double metric dimension (DMD), that can uniquely identify the location of any other node within the network. Utilizing DRSs can improve the accuracy and efficiency of the identification of the origin of a diffusion process. This ability is crucial for early intervention and control in scenarios such as epidemic outbreaks, misinformation spreading in social media, and fault detection in communication networks. In this study, we computed the DMD of flower snarks $J_m$ and quasi-flower snarks $G_m$ by describing their minimal doubly resolving sets (MDRSs). We deduce that the DMD for the flower snarks $J_m$ is finite and depends on the network's order, and the DMD for the quasi-flower snarks $G_m$ is finite and independent of the network's order. Furthermore, our findings offer valuable insights into the structural features of complex networks. This knowledge can offer direction for future studies in network theory and its practical implementations.