Let \(G=(V, E)\) be a graph and \({\mathbb {R}}\) be the set of real numbers. For a k-list total assignment L of G that assigns to each member \(z\in V\cup E\) a set \(L_{z}\) of k real numbers, a neighbor sum distinguishing (NSD) total L-coloring of G is a mapping \(\phi :V\cup E \rightarrow {\mathbb {R}}\) such that every member \(z\in V\cup E\) receives a color of \(L_z\), every pair of adjacent or incident members in \(V\cup E\) receive different colors, and \(\sum _{z\in E_{G}(u)\cup \{u\}}\phi (z)\ne \sum _{z\in E_{G}(v)\cup \{v\}}\phi (z)\) for each edge \(uv\in E\), where \(E_{G}(v)\) is the set of edges incident with v in G. In 2015, Pilśniak and Woźniak posed the conjecture that every graph G with maximum degree \(\Delta \) has an NSD total L-coloring with \(L_z=\{1,2,\dots , \Delta +3\}\) for any \(z\in V\cup E\), and confirmed the conjecture for all cubic graphs. In this paper, we extend their result by proving that every cubic graph has an NSD total L-coloring for any 6-list total assignment L.

令\（G =（V，E）\）为图，\（{\ mathbb {R}} \）为实数集。对于ķ -list总分配大号的ģ其分配给每个元件\（Z \ V中\杯Ë\）的一组\（L_ {Z} \）的ķ实数a邻居总和区分（NSD）总大号的-coloring ģ是一个映射\（\披：V \杯Ê\ RIGHTARROW {\ mathbb {R}} \） ，使得每个部件\（Z \ V中\杯ë\）接收的一个色\（L_z \ ），\（V \ cup E \）中的每对相邻或入射的成员接收不同的颜色，并且\（\ sum _ {z \ in E_ {G}（u）\ cup \ {u \}} \ phi（z）\ ne \ sum _ {z \ in E_ {G}（v）\ cup \ {v \}} \披（Z）\）对于每个边缘\（UV \于E \） ，其中\（E_ {G}（v）\）是与该组边缘入射的v在ģ。在2015年，Pilśniak和Woźniak提出了一个猜想，即每个最大度数\（\ Delta \）的图G的NSD总L着色为\（L_z = \ {1,2，\ dots，\ Delta +3 \} \ ）对于任何\（z \ in V \ cup E \），并确认所有三次图的猜想。在本文中，我们通过证明每个立方图都有一个NSD总L-对任何6个列表的总赋值L着色，扩展了它们的结果。