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A topological index is a numerical parameter that represents the molecular structure of a compound based on its graph‐theoretical properties. It provides a means to describe the structure‐activity relationship, as well as the physicochemical properties of the compound. Topological indices are used in various scientific fields, including chemistry, biology, and computer science, to study and predict the behavior of molecules. In this study, we concentrate on the calculation of M‐polynomials and entropy for the allotropic form of carbon, diamond. Algebraic operations are applied to these polynomials to obtain degree‐dependent topological invariants. [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]