1 Introduction  
2 Complexity  
3 Subcubic Graphs  
4 Bipartite Graphs  
Table 1: The values of $\chi_{st}^{\prime}(K_{m,n})$ for $m\in\{4,5,6,7,8\}$ and $n\leq12$.  
5 Planar Graphs  
6 List Star Edge-Coloring of Graphs  
7 Another Family of Graphs