Graphene Graphene Graphene is an allotrope (form) of carbon consisting of a single layer of carbon atoms arranged in a hexagonal lattice. It is a semimetal with small overlap between the valence and the conduction bands (zero bandgap material).<ref name="10.1002/adma.201502544 p.6519-6525"></ref> It is the basic structural element of many other allotropes of carbon, such as graphite, diamond, charcoal, carbon nanotubes and fullerenes. Graphene has many uncommon properties. It is the strongest material ever tested, conducts heat and electricity efficiently, and is nearly transparent. Graphene shows a large and nonlinear diamagnetism, greater than that of graphite, and can be levitated by neodymium
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