A proper edge coloring of a graph G is strict neighbor-distinguishing if for any two adjacent vertices u and v, the set of colors used on the edges incident to u and the set of colors used on the edges incident to v are not included with each other. The strict neighbor-distinguishing index of G is the minimum number \(\chi '_\mathrm{snd}(G)\) of colors in a strict neighbor-distinguishing edge coloring of G. In this paper, we prove that every connected subcubic graph G with \(\delta (G)\ge 2\) has \(\chi '_\mathrm{snd}(G)\le 7\), and moreover \(\chi '_\mathrm{snd}(G)=7\) if and only if G is a graph obtained from the graph \(K_{2,3}\) by inserting a 2-vertex into one edge.

如果对任意两个相邻顶点u和v而言，图G的适当边缘着色是严格的邻域区分，则不包括在入射到u的边缘上使用的颜色集合和在入射到v的边缘上使用的颜色集合彼此。的严格邻居区分索引ģ是最小数目\（\志“_ \ mathrm {SND}（G）\）在严格的邻居区分边缘的着色的颜色ģ。在本文中，我们证明了每个已连接的subcubic图ģ与\（\增量（G）\ GE 2 \）具有\（\志“_ \ mathrm {SND}（G）\文件7 \） ，而且\（\ chi'_ \ mathrm {snd}（G）= 7 \）当且仅当G是通过将2个顶点插入一个边而从图\（K_ {2,3} \）获得的图。