Induced H-packing k-partition number for certain nanotubes and chemical graphs

Abstract

Nanotechnology stands forefront in the science research and technology development. Carbon Nanocones and Carbon nanotubes (CNTs) are one of the most promising materials in the field of nanotechnology. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. An $$\textit{H}$$-packing of a graph $$\textit{G}$$ is the set of vertex disjoint subgraphs of G, each of which is isomorphic to a fixed graph $$\textit{H}$$. In this paper we determine a $$\textit{H}$$-packing and an induced $$\textit{H}$$-packing k-partition number for V-Phenylenic Nanotube, $$\textit{H}$$-Naphtalenic Nanotube, $$\textit{H}$$-Anthracenic Nanotube, $$\textit{H}$$-Tetracenic nanotube, $$CNC_{3} [n]$$ Nanocone and Circum Tetracene with $$\textit{H}\simeq \textit{P}_{3}$$.