Bounds on the partition dimension of one pentagonal carbon nanocone structure

The partition dimension is the most complicated resolving parameter of all the resolvability parameters. In this parameter, the vertex set of a graph is completely subdivided into subsets so that each vertex of a graph has a unique identification in terms of the partitioning of its selected subsets. In this paper, we consider Carbon nanocone structure (CNC) more specifically one pentagonal carbon nanocone CNCζ,5. It is also regarded as a useful structure in terms of various applications. To delve deeper into this structure, we provide a graphical representation of it and identified sharp bounds for the partition dimension. We conclude that the pentagonal carbon nanocone CNCζ,5 has partition dimension ≤4.