m个长为14的圈的不交并的点可区别Ⅰ-全染色

Vertex-distinguishing Ⅰ-total colorings of mC14

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构造具体染色的方法,证明mC_(14)的最优点可区别Ⅰ-全染色及最优点可区别Ⅵ-全染色,确定图mC_(14)的点可区别Ⅰ-全色数和点可区别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mC_(14)成立。

The problems of the optimal vertex-distinguishingⅠ-total colorings(VDITC)and the optimal vertex-distinguishingⅥ-total colorings(VDVITC)of graph mC_(14) are proved by constructing a matrix which is composed of color sets and empty set as the elements and using the methods of distributing color sets in advance and describing coloring explicitly.Thus vertex-distinguishingⅠ-total chromatic numbers and the vertex-distinguishingⅥ-total chromatic numbers of graph mC_(14) are determined.The results show that the VDITC conjecture and VDVITC conjecture are valid for graph mC_(14).