On metric dimension of carbon nanotube Y-junctions

Carbon nanotube Y-shaped junctions (normally called as Y-junctions) are constructed by inserting heptagons into the graphene sheet. The design requires the inclusion of at least 6 heptagons at the junction where 3 carbon nanotubes joined. With the growing focus on carbon nanotubes, their junctions have garnered increased attention for their applications in various scientific fields. Chemical structures can be expressed in graphs, where atoms represent vertices, and the bonds between the atoms are called edges. To obtain the exact position of an atom, which is unique from all the atoms, several atoms are selected, this is called resolving set. The minimum number of atoms in the resolving set is called the metric dimension. In this paper, we have computed the metric dimension of carbon nanotube Y-junctions, assigning each atom a unique identifier to facilitate precise location. The metric dimension is constant for all the values of the 3 parameters included to develop a Y-junction. It resulted in 3 metric dimensions for the entire Y-junction. It means that whatever the order and quantity of nanotubes attached to it, the metric dimension will remain constant with number 3.