幂图的点强全色数

On the Vertex Strong Total Chromatic Number of Power Graph

图G的一个正常全染色称为图G的点强全染色,当且仅当N[v]中任意元素都染有不同的颜色,其中N[v]={u|uv∈E(G)}∪{v},图G的点强全染色所用颜色的最少数目称为图G的点强全色数.文章通过研究幂图Pk n的结构性质,利用穷染、置换的方法,研究了幂图Pk n的点强全色数,并给出了一种具体的染色方案.

A proper total coloring of the graph G is said to be a vertex strong total coloring, if and only if any element in N[v] are colored with different colors, where N[v] = t u I uv E E（G）/ U {v}. The least number of the vertex strong colors is called the vertex strong total chromatic number. According to the properties of power graph, using color one by one and recursion, the vertex strong total coloring chromatic number of power graph Pkn is studied, at the same time, a coloring method is given.