Bi-Edge Metric Dimension of Graphs

Rinurwati Rinurwati, Fadillah Dian Maharani


Given a connected G = (V(G),E(G)) graph. The main problem in graph metric dimensions is calculating the metric dimensions and their characterization. In this research, a new dimension concept is introduced, namely a bi-edge metric dimension of graph which is a development of the concpet of bi-metric graphs with the innovation of bi-metric graph representations to become the bi-edge metric graph representations. In this case, what is meant by bi-edge metric and edge detour. If there is a set in G that causes every edge in G has a different bi-edge metric representation in G, then that set is called the biedge metric resolving set. The minimum cardinality of the bi-edge metric resolving set graphs is called the bi-edge metric dimension of G graph, denoted by edimb(G). The spesific purpose of this research is to apply the concept of bi-edge metric dimensions to special graphs, such as cycle, complete, star and path can be obtained.


Bi-Metric Dimension; Edge Metric Dimension; Edge Detour Dimension; Bi-Edge Metric Dimension

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