m个阶为4的圈的不交并的点可区别Ⅰ-全染色和Ⅵ-全染色

Vertex-distinguishing Ⅰ-total colorings and vertex-distinguishing Ⅵ-total colorings of m C4

讨论了m个阶为4的圈的点不交的并图m C 4的点可区别I-全染色和点可区别VI-全染色.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给出了m C 4的最优点可区别I-全染色以及最优点可区别VI-全染色,进而确定了图m C 4的点可区别I-全色数及点可区别VI-全色数.结论表明点可区别I-全染色猜想和点可区别VI-全染色猜想对图m C 4成立.

The problem of the vertex distinguishing I-total colorings(VDITC)and vertex distinguishing VI-total colorings(VDVITC)of the disjoint union m C 4 of m cycles of order 4 are discussed in this paper.By using the methods of constructing a matrix which is composed of color sets and empty set as the elements,distributing color sets in advance and coloring explicitly,we give the optimal vertex-distinguishing I-total colorings and the optimal vertex-distinguishing VI-total colorings of mC 4.Thus vertex-distinguishing I-total chromatic numbers and the vertex-distinguishing VI-total chromatic numbers of m C 4 are determined.Results in this paper show that the VDITC conjecture and VDVITC conjecture are valid for m C 4.