Computational analysis of face neighbourhood index of carbon nanocones

Abstract In recent years, nanomaterials such as carbon nanotubes, nanocones, boron nanowires and nanoclusters have been widely studied because of their unique structures and useful electronic properties. Among them carbon based nanostructures are especially important for applications in nanotechnology. To study these materials graph theory provides different numerical measures that describe their structure. One such measure is the face neighbourhood index which not only counts the faces in a planar graph but also considers how they are connected through the vertices on their boundaries. This makes it a more detailed tool than earlier indices for understanding molecular geometry. In this work, we calculate a generalized form of the face neighbourhood index for carbon nanocones CNC m [n]. These results can help researchers better explain the physical and chemical behavior of nanocones and guide future applications in nanoscience.