A k-edge-weightingw of a graph G is an assignment of an integer weight, w(e) ∈ {1, …, k}, to each edge e. An edge-weighting naturally induces a vertex coloring c by de?ning for every u ∈ V (G). A k-edge-weighting of a graph G is vertex-coloring if the induced coloring c is proper, i.e., c(u) ≠ c(v) for any edge uv ∈ E(G). When k ≡ 2 (mod 4) and k≥6, we prove that if G is k-colorable and 2-connected, δ(G)≥k - 1, then G admits a vertex-coloring k-edge-weighting. We also obtain several suffcient conditions for graphs to be vertex-coloring k-edge-weighting.