Edge Metric Dimension on Some Families of Tree
Robiatul Adawiyah, Dafik Dafik, Ridho Alfarisi, Rafiantika Megahnia Prihandini, Ika Hesti Agustin · Journal of Physics Conference Series · 2019
Metric Dimension as a graph invariant has various applications in real life. One of the metric dimension application is for the navigation system in transportation. In this Paper, we continue to develop the study of edge metric dimension. Let G = ( V , E ) be a connected graph with v ∈ V and e = uw ∈ E . The distance between the vertex v and the edge e is given by d G ( e , v ) = min { d ( u , v ), d ( w , v )}. A vertex w ∈ V distinguishes two edges e 1 e 2 ∈ E if d G ( w , e 1 ≠ d G ( w , e 2 )). A set S of vertices in a connected graph G is an edge metric generator for G if every two edges of G are distinguished by some vertices of S . The edge metric dimension of G , denoted by dim E ( G ), is the minimum cardinality of edge metric generator for G . As a main result, we provide some results of edge metric dimension on some families of tree graph, namely star graph, broom graph, double broom graph, and banana tree graph.