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Mesh generation is an important step inmany numerical methods.We present the “HierarchicalGraphMeshing” (HGM)method asa novel approach to mesh generation, based on algebraic graph theory.The HGM method can be used to systematically constructconfigurations exhibiting multiple hierarchies and complex symmetry characteristics. The hierarchical description of structuresprovided by the HGM method can be exploited to increase the efficiency of multiscale and multigrid methods. In this paper, theHGMmethod is employed for the systematic construction of super carbon nanotubes of arbitrary order, which present a pertinentexample of structurally and geometrically complex, yet highly regular, structures. The HGMalgorithm is computationally efficientand exhibits good scaling characteristics. In particular, it scales linearly for super carbon nanotube structures and is working muchfaster than geometry-based methods employing neighborhood search algorithms. Its modular character makes it conducive toautomatization. For the generation of a mesh, the information about the geometry of the structure in a given configuration isadded in a way that relates geometric symmetries to structural symmetries. The intrinsically hierarchic description of the resultingmesh greatly reduces the effort of determining mesh hierarchies for multigrid and multiscale applications and helps to exploitsymmetry-related methods in the mechanical analysis of complex structures

Meshing Highly Regular Structures: The Case of Super Carbon Nanotubes of Arbitrary Order