Let \(G=(V(G),E(G))\) be a connected graph. A set of vertices \(S\subseteq V(G)\) is an edge metric generator of G if any pair of edges in G can be distinguished by their distance to a vertex in S. The edge metric dimension edim(G) is the minimum cardinality of an edge metric generator of G. In this paper, we first give a sharp bound on \(edim(G-e)-edim(G)\) for a connected graph G and any edge \(e\in E(G)\). On the other hand, we show that the value of \(edim(G)-edim(G-e)\) is unbounded for some graph G and some edge \(e\in E(G)\). However, for a unicyclic graph H, we obtain that \(edim(H)-edim(H-e)\le 1\), where e is an edge of the unique cycle in H. And this conclusion generalizes the result on the edge metric dimension of unicyclic graphs given by Knor et al. Finally, we construct graphs G and H such that both \(edim(G)-edim(G-u)\) and \(edim(H-v)-edim(H)\) can be arbitrarily large, where \(u\in V(G)\) and \(v\in V(H)\).

令\(G=(V(G),E(G))\)是一个连通图。一组顶点的\（S \ subseteq V（G）\）是的边缘度量产生ģ如果在任何一对边缘ģ可以通过它们的距离来区分在一个顶点小号。边缘度量尺寸EDIM（ģ）是边缘度量产生器的最小基数ģ。在本文中，我们首先针对连通图G和任何边\(e\in E(G)\)给出了\(edim(Ge)-edim(G)\)的尖锐边界。另一方面，我们证明\(edim(G)-edim(Ge)\) 的值对于某些图G是无界的和一些边缘\(e\in E(G)\)。然而，对于单环图H，我们得到\(edim(H)-edim(He)\le 1\)，其中e是H 中唯一环的边。并且该结论概括了Knor等人在单环图的边度量维度上的结果。最后，我们构造图G和H，使得\(edim(G)-edim(Gu)\)和\(edim(Hv)-edim(H)\)都可以是任意大的，其中\(u\in V (G)\)和\(v\in V(H)\)。