Central Metric Dimension of the Generalized k –corona G⊙kℋ

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 text]corona [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].