图的邻和可区别染色

n edge~$[k]$-coloring of a graph~$G$ is an edge coloring of~$G$ by using the color set~$[k]={1,2,cdots,k}$. Let~$f(v)$ denote the sum of the colors of all incident edges of~$v$. An edge~$[k]$-neighbor sum distinguishing-coloring of~$G$ is anedge~$[k]$-coloring of~$G$ such that for each edge~$uvin E(G)$,~$f(u) eq f(v)$. In such a coloring, the smallest value~$k$ is called neighbor sum distinguishing edgechromatic number, denoted by~$chi^{'}_{sum}(G)$. Similarly, we can define total~$[k]$-neighbor sum distinguishing-coloring, and denote neighbor sum distinguishing totalchromatic number by~$chi^{''}_{sum}(G)$. The rapid development of computer technology vigorously promote the development of the coloring problem in graph theory.In recent years, neighbor sum distinguishing coloring attracted widespread attention, this article introduces some progress and conclusions about the neighbor sum distinguishing coloring.