Adjacent-vertex-distinguishing proper edge colorings of planar bipartite graphs with Δ=9,10, or 11

It is obtained in this paper by using of discharging method that the adjacent-vertex-distinguishing proper edge chromatic number χa′(G)≤Δ(G)+1 for any planar bipartite graph G with maximum degree Δ(G)=9,10, or 11 and no component K2. This expands a result which belongs to K. Edwards, M. Horňák, M. Woźniak.