Farooq Umar, Abbas Wasim, Chaudhry Faryal, Azeem Muhammad, Almohsen Bandar
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
Department of Mathematics, Riphah International University, Lahore, Pakistan.
PLoS One. 2025 Mar 4;20(3):e0316376. doi: 10.1371/journal.pone.0316376. eCollection 2025.
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.
本研究探讨了二氧化硅纳米结构，特别是纳米片、纳米管和纳米环的度量维数（MD）和边度量维数（EMD）。度量维数描述了唯一标识图中其他每个点所需的最少顶点数。相比之下，边度量维数是区分每条边所需的最少顶点数。了解这些维数对于表征纳米颗粒的几何和结构特性至关重要。利用图论技术，我们计算了各种二氧化硅纳米结构的MD和EMD，以阐明它们独特的几何形状和构型。我们的研究结果给出了这些维数的精确公式，这对于设计和优化具有特定性能的二氧化硅基材料至关重要。本研究为化学、材料科学和纳米技术领域的应用提供了有价值的见解，在这些领域中，纳米尺度结构特征的知识至关重要。
