Liu Peide, Ali Sikander, Azeem Muhammad, Kamran Jamil Muhammad, Zahid Manzoor Ahmad, Ali Waleed, Almohsen Bandar
School of Business Administration, Shandong Women's University, Jinan, 250300, Shandong, China.
School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250014, Shandong, China.
Sci Rep. 2024 Nov 3;14(1):26536. doi: 10.1038/s41598-024-77697-9.
The mixed metric dimension of a graph is an important parameter in characterizing its structural complexity, specifically in nanoscale networks where precision is paramount. In this article, we calculate the mixed metric dimension of hexagonal nano-network, a modal with significant applications in nanotechnology and material science. Through rigorous analysis, we set up that the mixed metric dimension of the hexagonal nano-network is exactly three, highlighting its minimal but enough resolving set that uniquely identifies all vertices. Furthermore, we check out the exchange property within this context, demonstrating the robust adaptability of the hexagonal network's resolving sets. Our findings display that the alternate assets aren't the handiest preserved but stronger in these nano-networks, allowing for flexible adjustments in resolving sets without compromising the network's integrity. This examination offers critical insights into the fundamental properties of hexagonal nano-networks, offering a theoretical foundation for future research in nanomaterial design and optimization. The results underscore the potential of leveraging mixed metric dimensions and exchange properties to achieve efficient and scalable solutions in nano-network applications.
图的混合度量维数是表征其结构复杂性的一个重要参数，特别是在精度至关重要的纳米尺度网络中。在本文中，我们计算了六边形纳米网络的混合度量维数，该模型在纳米技术和材料科学中有重要应用。通过严格分析，我们确定六边形纳米网络的混合度量维数恰好为三，突出了其最小但足够的分辨集，该分辨集能唯一识别所有顶点。此外，我们在这种情况下研究了交换性质，证明了六边形网络分辨集的强大适应性。我们的研究结果表明，在这些纳米网络中，交替资源不仅得以保留，而且更强，这使得在不损害网络完整性的情况下，分辨集能够灵活调整。这项研究为六边形纳米网络的基本性质提供了重要见解，为纳米材料设计和优化的未来研究提供了理论基础。结果强调了利用混合度量维数和交换性质在纳米网络应用中实现高效和可扩展解决方案的潜力。
