图mC_(8)的点可区别Ⅰ-全染色和Ⅵ-全染色

Vertex-DistinguishingⅠ-Total Colorings andVertex-DistinguishingⅥ-Total Colorings of Graph mC_(8)

通过构造以色集合和空集为元素的矩阵,利用色集合事先分配法及具体的染色方案,给出图mC_(8)的最优点可区别Ⅰ-全染色和最优点可区别Ⅵ-全染色,进而确定图mC_(8)的点可区别Ⅰ-全色数和点可区别Ⅵ-全色数.结果表明,VDITC猜想和VDVITC猜想对图mC_(8)成立.

By constructing a matrix which was composed of color sets and empty set as the elements,using t he distributing method of color sets in advance and specific coloring scheme,we gave the best vertex-distinguishing Ⅰ-total colorings(VDITC)and the best vertex-distingui shing Ⅵ-total colorings(VDVITC)of graph mC_(8).Thus vertex-distinguishing Ⅰ-total chromatic numbers and the vertex-distinguishing Ⅵ-total chromatic numbers of graph mC_(8)were determined.The results show that the VDITC conjecture and VDVITC conjecture are valid for graph mC_(8).