The Central Metric Dimension of the k-Corona Graph

The metric dimension is the minimum cardinality of a subset of the vertex set of a graph G that uniquely represents each vertex in a graph. The central set is a set of vertices with minimum eccentricity. This central set concept can be used to determine strategic public service locations, such that accessible transportation can be reached from all regions. The central metric dimension is the minimum cardinality of a resolving set that includes the central set. This study aims to determine the central metric dimension in k-corona graph. The k-corona operation of G and H denoted by G ⊙k H is a generalization of the corona operation, where a new graph is formed by connecting each vertex of a graph G to k copies of graph H. The results show that the central metric dimension of the k-corona graph depends on the central set of G, the order of G, the value of k, and the metric dimension of H.