Mechanical properties of carbon nanotubes Mechanical properties of carbon nanotubes The mechanical properties of carbon nanotubes reveal them as one of the strongest materials in nature. Carbon nanotubes (CNTs) are long hollow cylinders of graphene. Although graphene sheets have 2D symmetry, carbon nanotubes by geometry have different properties in axial and radial directions. It has been shown that CNTs are very strong in the axial direction. Young's modulus on the order of and tensile strength of were obtained. Carbon nanotubes are the strongest and stiffest materials yet discovered in terms of tensile strength and elastic modulus respectively. This strength results from the covalent sp bonds
Thickness (graph theory) Thickness (graph theory) In graph theory, the thickness of a graph is the minimum number of planar graphs into which the edges of can be partitioned. That is, if there exists a collection of planar graphs, all having the same set of vertices, such that the union of these planar graphs is , then the thickness of is at most . In other words, the thickness of a graph is the minimum number of planar subgraphs whose union equals to graph . Thus, a planar graph has thickness 1. Graphs of thickness 2 are called biplanar graphs. The concept of