The act of accessing the exact location, or position, of a node in a network is known as the localization of a network. In this methodology, the precise location of each node within a network can be made in the terms of certain chosen nodes in a subset. This subset is known as the locating set and its minimum cardinality is called the locating number of a network. The generalized hexagonal cellular network is a novel structure for the planning and analysis of a network. In this work, we considered conducting the localization of a generalized hexagonal cellular network. Moreover, we determined and proved the exact locating number for this network. Furthermore, in this technique, each node of a generalized hexagonal cellular network can be accessed uniquely. Lastly, we also discussed the generalized version of the locating set and locating number.

Coronoid systems actually arrangements of hexagons into six sides of benzenoids. By nature, it is an organic chemical structure. Hollow coronoids are primitive and catacondensed coronoids. It is also known as polycyclic conjugated hydrocarbons. The mathematical study of chemicals is of great interest to different specialties researchers. While graph theory always played a significant role to make chemical structures understandable and blessed with applications also. After transforming the chemical structure into a graph, one can implement different theoretical and implicative studies on structures. Metric dimension is considered as one of the most studied and implicative parameters of graph theory. In this concept, few suggested vertices are chosen such as the remaining vertices have unique locations or identifications. In this study, we discussed different metric-based parameters for the hollow coronoid structure.

A carbon nanotube is made up of a molecular structure of a regular hexagonal lattice. This tube can be extended by closing one- or both end of the tube, denoted by semi-capped and capped nanotube. Due to its different structures, it is categorized into three forms, despite every form or shape, it has a wide range of usage. As a memory device, current-carrying device, regenerative study of medicines, and highly recommended in tissue engineering. Due to its numerous applications, there is immense interest to study its physical and chemical properties. As nanotube and its shape is motivated by a molecular structure and topological descriptors are also tools to study different molecular structures, we use this tool to analyze different nanotube structures like armchair carbon, semi-capped, and capped nanotube by Zagreb indices and its co-indices. Moreover, we also compared capped (semi or full) and uncapped armchair carbon nanotube and provided sufficient results of the comparison.

The concept of M‐polynomials determines the algebraic form of a system or network. It creates a structure into an algebraic equation and makes work easy to do on such a structure. This has diverse uses in different applied mathematics and as well as in engineering fields. In this study, we look closely at the abstract form of Y‐shaped junctions. For the generic view of Y‐shaped junctions, we developed some vertex‐degree‐based M‐polynomials formulas. On Y‐shaped junctions, we discussed some topological index‐based concepts as well and verified the results available in the literature.

The production of low-cost, small in size, and high in efficiency objects is the topic of research in almost all scientific fields, especially of engineering. In this scenario, nanotechnology becomes of great importance. To achieve these tasks, one needs to study the different physical and chemical aspects of a chemical compound. In mathematical graph theory, chemical compounds are transformed in a unique mathematical representation and then examined under various parameters for these purposes. The Partition Dimension is also one of these parametric tools, which are used to identify each atom or vertex of a chemical structure under some chosen conditions. In the present paper, we use this tool to show the unique identification of each atom of a tri-hexagonal lattice of the $\alpha $ -boron nanotube.