New Strategies for Hierarchical Honeycomb Meshes
Burhan Selçuk Ayşe Nur Altintaş Tankül Saliha Özgüngör Ali Karcı
AbstractIn nature, the honeycomb structure is a recurring phenomenon that is admired for its efficiency, durability, and optimum utilization of space. These qualities have inspired the development of man-made honeycomb structures, which are widely applied in various fields, including engineering, architecture, and materials science. Among these applications, the use of honeycomb networks offers significant advantages in constructing hierarchical structures, such as enhanced scalability, robustness, and geometric flexibility. In this paper, we investigate labeling and Hamiltonian path algorithms specifically designed for Hierarchical Honeycomb Networks (HHMs) by presenting a novel strategy. The proposed labeling algorithm systematically generates the coordinates of HHM nodes at multiple hierarchical levels, utilizing an recursive approach to ensure consistency and efficiency. Additionally, we investigate a Hamiltonian feature with the same algorithm designed to define a path that visits each node exactly once within the HHM framework. This study demonstrates, through theoretical analysis and algorithmic implementation, the effectiveness of the new strategy in optimizing the construction and traversal of HHM, providing potential insights for applications in network design, computational geometry, and spatial data organization.