Induced H-packing k-partition problem in certain carbon based nanostructures

Nanotechnologyhasgainedrecentlymuchattentioninresearchtodevelopnewcarbon based materials with unique properties. It generates many new materials and devices with a wide range of applications in medicine, electronics, and computer. Carbon nanotubes (CNTs) are one of the most promising resources in the field of nanotech nology. Mathematically, assembling in predictable arrays is equivalent to packing in graphs. An H-packingofagraph G isthesetofvertexdisjointsubgraphsof G,eachof which is isomorphic to a fixed graph H. In this paper we determine perfect and almost perfect H-packing and an induced H-packing k-partition number for Armchair car
bon nanotube ACNT[n,m], Zigzag carbon nanotube ZCNT[n,m], Zigzag polyhex carbon nanotube TUHC6[2m,n], Boron triangular carbon nanotubes BNTt[n,m], TUC4C8(R), TUC4C8(S), HAC5C6C7[n,m] and HAC5C7[n,m] with H isomor
phic to P3. Further we investicate C4-packing for TUC4C8(R)