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\begin{document}$$\textit{G}$$\end{document} be a simple graph with no isolated edges. The neighbor-distinguishing edge coloring of G\documentclass[12pt]{minimal}
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\begin{document}$$\textit{G}$$\end{document} is a proper edge coloring of G\documentclass[12pt]{minimal}
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\begin{document}$$\textit{G}$$\end{document} such that any pair of adjacent vertices have different sets consisting of colors assigned on their incident edges. The neighbor-distinguishing index of G\documentclass[12pt]{minimal}
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\begin{document}$$\textit{G}$$\end{document}, denoted by χa′(G)\documentclass[12pt]{minimal}
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\begin{document}$$\chi '_{a}(G)$$\end{document}, is the minimum number of colors in such an edge coloring of G\documentclass[12pt]{minimal}
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\begin{document}$$\textit{G}$$\end{document}. In this paper, we show that if G\documentclass[12pt]{minimal}
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\begin{document}$$\textit{G}$$\end{document} is a connected planar graph with maximum degree Δ≥14\documentclass[12pt]{minimal}
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\begin{document}$$\Delta \ge 14$$\end{document}, then Δ≤χa′(G)≤Δ+1\documentclass[12pt]{minimal}
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\begin{document}$$\Delta \le \chi '_a(G)\le \Delta +1$$\end{document}, and χa′(G)=Δ+1\documentclass[12pt]{minimal}
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\begin{document}$$\chi '_a(G)=\Delta +1$$\end{document} if and only if G\documentclass[12pt]{minimal}
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\begin{document}$$\textit{G}$$\end{document} contains a pair of adjacent vertices of maximum degree. This improves a result in [W. Wang, D. Huang, A characterization on the adjacent vertex distinguishing index of planar graphs with large maximum degree, SIAM J. Discrete Math. 29(2015), 2412–2431], which says that every connected planar graph G\documentclass[12pt]{minimal}
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\begin{document}$$\textit{G}$$\end{document} with Δ≥16\documentclass[12pt]{minimal}
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\begin{document}$$\Delta \ge 16$$\end{document} has Δ≤χa′(G)≤Δ+1\documentclass[12pt]{minimal}
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\begin{document}$$\Delta \le \chi '_a(G)\le \Delta +1$$\end{document}, and χa′(G)=Δ+1\documentclass[12pt]{minimal}
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\begin{document}$$\chi '_a(G)=\Delta +1$$\end{document} if and only if G\documentclass[12pt]{minimal}
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\begin{document}$$\textit{G}$$\end{document} contains a pair of adjacent vertices of maximum degree.
