Exploring metric dimension of nanosheets, nanotubes, and nanotori of SiO2

This work investigates the metric dimension (MD) and edge metric dimension (EMD) of SiO2 nanostructures, specifically nanosheets, nanotubes, and nanotorii. The metric dimension describes the minimum number of vertices required to uniquely identify every other point in a graph. In contrast, the edge metric dimension is the minimum number of vertices needed to distinguish each edge. Understanding these dimensions is essential for characterizing the geometric and structural properties of nanoparticles. Using graph theory techniques, we compute the MD and EMD of various SiO2 nanostructures to elucidate their unique geometries and configurations. Our findings offer precise formulas for these dimensions, critical for designing and optimizing SiO2-based materials with targeted properties. This study provides valuable insights for applications in chemistry, materials science, and nanotechnology, where knowledge of structural characteristics at the nanoscale is crucial.