中文摘要：

设φ为图G的正常k-边染色。对任意v∈V（G）,令f_φ（v）=Σuv∈E（G）φ（uv）。若对每条边uv∈E（G）都有f_φ（u）≠f_φ（v）,则称φ为图G的k-邻和可区别边染色。图G存在k-邻和可区别边染色的k的最小值称为G的邻和可区别边色数,记作χ＇_Σ（G）。确定了一类稀疏图的邻和可区别边色数,得到：若图G不含孤立边,Δ≥6且mad（G）≤5/2,则χ＇_Σ（G）=Δ当且仅当G不含相邻最大度点。

英文摘要：

Let φ be a proper k-edge coloring of G. For each vertex v∈V（G）,set fφ（v）=Σuv∈E（G）φ（uv） ,φ is called ak-neighbor sum distinguishing edge coloring of G if fφ（u）≠fφ（v）for each edge uv E（G）. The smallest k such that G has a k-neighbor sum distinguishing edge coloring is called the neighbor sum distinguishing index, denoted by χ＇Σ（G）The neighbor sum distinguishing index of a kind of sparse graphs is determined. It is proved that if G is a graph without isolated edges, △≥ 6 and mad （G）≤5/2,then χ＇_Σ（G）=Δif and only if G has no adjacent vertices ofmaximum degree.