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Adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for the proper edge-coloring of [Formula: see text] in which no two adjacent vertices are incident to edges colored with the same set of colors. The minimum number of colors required for an adjacent vertex-distinguishing proper edge-coloring of [Formula: see text] is called the adjacent vertex-distinguishing proper edge-chromatic index. Adjacent vertex-distinguishing proper edge-chromatic indices of the middle graph, splitting graph and shadow graph of path and cycle are determined. Adjacent vertex-distinguishing proper edge-chromatic indices of the triangular grid [Formula: see text], [Formula: see text]-graph and generalized [Formula: see text]-graph are also determined.