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A vertex $w\\in V$ distinguishes two edges $e_1,e_2\\in E$ if $d_G(w,e_1)\\ne d_G(w,e_2)$. 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 vertex of $S$. The smallest cardinality of an edge metric generator for $G$ is called the edge metric dimension and is denoted by $edim(G)$. 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