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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]

Recent findings of diverse forms of carbon nanostructures have encouraged research on their applications in several areas. They are used as a structural material in electronic and optical devices, involving transistors, photodetectors, plastic, biological sensors, pharmaceutical and medicine, and drug delivery systems. Since the discovery of Y‐shaped carbon nanotubes (CNTs) junctions, they have drawn interest for future electron devices, for example, three‐terminal transistors, amplifiers, and switches. A topological index is a number that is used to study the physicochemical properties of chemical structures. In this paper, we are providing topological properties of CNT Y‐junctions. The results obtained for different types of Y‐junction graphs appeared with comparisons. According to the best of our knowledge and literature, this is the first report about topological indices on this class of CNT junctions. [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]