A vertex v in a connected graph G strongly distinguishes two edges e1 and e2 if d(e1, v) = d(e2, v) + d(e1, e2) or d(e2, v) = d(e1, v) + d(e1, e2), where for an edge e = xy, d(e, v) = min{d(x, v), d(y, v)} and also the distance between two edges e1 = xy and e2 = uv is d(e1, e2) = min{d(e1, u), d(e1, v)}. A nonempty set S ⊆ V (G) is a strong edge metric generator of a graph G if for any two distinct edges e1, e2 ∈ E(G), there exists a vertex s ∈ S such that s strongly distinguishes e1 and e2. A strong edge metric generating set with the smallest number of elements is called a strong edge metric basis of G and the number of elements in a strong edge metric basis is called the strong edge metric dimension of G and it is denoted by sedim(G). In this paper, we propose this concept as an extension of the strong metric dimension and we determine the strong edge metric dimension of several classes of graphs. Moreover, the sedim for the G-generalized join graph is investigated. Furthermore, we study the strong edge metric dimension of the comaximal graph of the ring of integers modulo n. Finally, we pose an integer linear programming model for finding the strong edge metric dimension of graphs.

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