For edges \(e\) and \(f\) in a connected graph \(G\), the distance \(d(e, f)\) between \(e\) and \(f\) is the minimum nonnegative integer \(n\) for which there exists a sequence \(e = e_0, e_1, \ldots, e_l = f\) of edges of \(G\) such that \(e_i\) and \(e_{i+1}\) are adjacent for \(i = 0, 1, \ldots, l-1\). Let \(c\) be a proper edge coloring of \(G\) using \(k\) distinct colors and let \(D = \{C_1, C_2, \ldots, C_k\}\) be an ordered partition of \(E(G)\) into the resulting edge color classes of \(c\). For an edge \(e\) of \(G\), the color code \(c_D(e)\) of \(e\) is the \(k\)-tuple \((d(e, C_1), d(e, C_2), \ldots, d(e, C_k))\), where \(d(e, C_i) = \min\{d(e, f): f \in C_i\}\) for \(1 \leq i \leq k\). If distinct edges have distinct color codes, then \(c\) is called a resolving edge coloring of \(G\). The resolving edge chromatic number \(\chi_{re}(G)\) is the minimum number of colors in a resolving edge coloring of \(G\). Bounds for the resolving edge chromatic number of a connected graph are established in terms of its size and diameter and in terms of its size and girth. All nontrivial connected graphs of size \(m\) with resolving edge chromatic number \(3\) or \(m\) are characterized. It is shown that for each pair \(k, m\) of integers with \(3 \leq k \leq m\), there exists a connected graph \(G\) of size \(m\) with \(\chi_{re}(G) = k\). Resolving edge chromatic numbers of complete graphs are studied.
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