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Due to the recent economic crisis of the world, producing low-cost objects in every field of science and engineering is the main topic of research. Making small in-sized objects, low in budget and weight, and efficient in quality is necessary for the present and future world. In this whole scenario, nanotechnology contributing more than enough. Nanomaterials and nano-objects are highly preferable, carbon nanotubes are one of the highly chosen structures of nanomaterials, which is used in different chemical, biological, and technological fields. This thought leads us to study its different aspects of physical and chemical properties. Topological descriptors are used to characterize different molecular structures by making its numerical quantitative analysis. This article deals with different carbon nanotube structures, studying their chemical and physical characterizations and comparing armchair, semicapped, and capped carbon nanotubes. It provides the best option by making comparative analysis with different tools and algorithms. [ABSTRACT FROM AUTHOR]

There are different mathematical tools to establish a numeric correlation between a chemical structure and its properties. A topological index is such a successful tool. It represents a graph in form of a single real number. In QSAR/QSPR study, the bioactivity of chemical compounds is predicted, using physico-chemical properties and topological indices. In this area of research, graph theory plays a vital role. The four operations on graphs were defined by Eliasi and Taeri in 2009. Imran et al. studied Cartesian product of the four operations on graph and computed bounds for some degree-based topological indices in 2017. In this paper, we extend this study for the lexicographic product of graphs to determine bounds of Zagreb indices, multiple Zagreb indices, and F-index for four sums of connected graphs. [ABSTRACT FROM AUTHOR]