Adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for the proper edge-coloring of G 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 G 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 Tn, H-graph and generalized H-graph are also determined.
