The central metric dimension of a graph is defined as the minimum cardinality of the resolving set containing the central vertex, ensuring that all vertices can be uniquely identified by their distances to this set. Conceptually, central metric dimension can be interpreted in the context of public services place, such that they have minimum costs from the aspect of transportation costs to get there. The results obtained in this research are the central metric dimension of Formula: see text for any Formula: see text and sequence of Formula: see text Central metric dimension of an arbitrary connected graph Formula: see text and a sequences of star graphs, complete graphs, and complete bipartite graphs Formula: see text in the generalized Formula: see textcorona Formula: see text depends by the value of Formula: see text, the number of central vertices of graph Formula: see text and the metric dimensions of the graphs in the sequence Formula: see text. In particular, cycle and path graphs are considered as wheel and fan graphs respectively, so that the central metric dimension is determined by the value of Formula: see text, the number of central vertices of graph Formula: see text, and the metric dimension of the cycle and path graphs joined with the graph Formula: see text.
Susilowati et al. (Fri,) studied this question.