The combination of the central set and resolving set of the generalized corona product graph

Graph theory is a part of mathematics that continues to experience significant development from a theoretical aspect, one of which is the theory of metric dimensions. The concept of the central metric dimension is a combination of the metric dimension and the central set of a graph. The central metric dimension of the graph G refers to the minimum number of edges in a resolver set that contains a central set, which is indicated by dimcen(G). Some graphs with a central metric dimension are path graphs, cycle graphs, complete graphs, and complete bipartite graphs. This research aims to determine the central metric dimension of the generalized corona product graph from a connected graph G and ℋ, where ℋ representing a sequence of n connected graph H1, H2, …, Hn. In this study, the graph sequence ℋ is a sequence of similar graphs, such as the graph sequence of the star graph and the graph sequence of the complete graph. Central metric dimension of the generalized corona product graph, denoted by dimcen(G ⊙ ℋ). The results of this study are: first, the central set of the generalized corona product of the graph G ⊙ ℋ is the central set of the graph G, second, dimcen(Cn⊙ℋ)=|V(G)|+Σmi=1n(|V(Smi|−2)⁠, for ℋ is a graph sequence of the star graph, third, dimcen(Pn⊙ℋ)={ 1+∑i=1n|V(Kmi)−1|,​​fornisanodd2+∑i=1n|V(Kmi)−1|,​​fornisaneven⁠, for Pn be path graph with order n ≥ 3 and ℋ is a graph sequence of the complete graph.