Didi Febrian, Mulyono, Beatrice Marpaung
Graph theory is a branch of mathematics that has many roles in solving human problems. Therefore, the topic of research on graph theory continues to grow. The metric dimension is one of the research topics in graph theory which is an NP Complete problem. Graph and the set =(). The representation of vertex towards is the distance from to each element in , written If each distinct point in G has a different representation of W, then W is called resolving set. The metric dimension of G is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex, denoted (). The application of the metric dimensions, one of which is to optimize the provision of threat detection tools at essential facilities. The purpose of this study is to determine the metric dimensions of a branched prism graph. The branched prism graph × !" ⊙#$ is a modified graph obtained by adding a korona operation to the prism graph × !" with the null graph #$. Based on the results of this study, the metric dimensions of the branched prism graph × ˙#$, × ˙#$) = 3 for = 1 and (× ˙#$) = 2((- 1) for 1. © 2022 American Institute of Physics Inc.. All rights reserved.
Department of Mathematics, Universitas Negeri Medan, North Sumatera, Indonesia
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