mC_7的点可区别全染色

Vertex-Distinguishing Total Coloring of mC_7

考虑m个长为7的圈点不交的并mC7的点可区别全染色问题.通过构造以色集合为元素的矩阵,利用色集合事先分配法及递归法确定染色,得出了mC_7的点可区别全色数的确切值.结果表明VDTC猜想对图mC_7成立.

We considered the problem of the vertex-distinguishing total colorings of the disjoint union mC7 of m cycles of length 7. By constructing a matrix which was composed of color sets as elements, the vertex distinguishing total coloring of raG7 was determined by using the methods of distributing color sets in advance and induction. We obtained the exact value of vertex-distinguishing total chromatic number of rnCT. The results show that the VDTC conjecture is valid for taCT.