The dominant metric dimension on the vertex amalgamation product graph

The dominant metric dimension is the result of the development of graph theory, especially in the study of metric dimensions. The purpose of this research is to determine the dominant metric dimension on the vertex amalgamation v0l and v02, which are terminal vertices of graphs Gl and G2, respectively. The terminal vertex is a certain vertex that is set to each element of the graph collection that is carried out by the vertex amalgamation product. The vertex amalgamation product in this research is carried out on several special graphs including a complete bipartite graphs, a cycle graphs, a complete graphs, and a star graphs. From this research, it is found that Ddim(Amal{Gl; G2, v0l; v02 }) is the sum of the dominant metric dimensions of graphs Gl and G2 minus one or minus two where Gl and G2 are a complete bipartite graphs, a cycle graphs, a complete graphs and a star graphs. The results of this research indicate that the value of the dominant metric dimension of the vertex amalgamation product graph is influenced by the dominant basis, the order of graphs Gl and G2, and the terminal points of graphs Gl and G2.