图K(r,2m)的邻点可区别全染色

On the adjacent vertex-distinguishing total coloring of K(r,2m)

在等完全r-部图全染色的研究中,首先确定了每部有2个点的完全r-部图的全色数;然后利用已得到的结果进一步研究每部有n个点的完全r-部图的全色数.采用上述思路研究了等完全r-部图的邻点可区别全染色,利用图分解的方法给出了每部有2个点的完全r-部图的邻点可区别全色数;并给出了每部有偶数个点的等完全r-部图的邻点可区别全色数.

In the study of the total coloring about the balanced complete r-partite graph, the total chromatic number of complete r-partite graph with two vertices on each partition had been given. The total chromatic number of complete r-partite graph with n vertices on each partition using the result had also been studied. The adjacent vertex-distinguishing total coloring of the balanced complete r-partite graph was considered. The adjacent vertex-distinguishing total chromatic number of the complete r-partite graph with two vertices on each partition by the method of graph decomposition was given, and then the adjacent vertex-distinguishing total chromatic number of the balanced complete r-partite graph with even vertices on each partition was obtained.