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.