两类4-正则循环图的邻点可区别全色数

Adjacent-vertex-distinguishing total chromatic numbers on two classes of 4-regular cyclic graphs

设G是阶数不小于2的连通图,则其邻点可区别全染色是指G中任意两个相邻的顶点有不同的颜色和色集合,且任意相邻的两条边及一个顶点与其关联边的颜色也不相同.给出了两类邻接矩阵的第一行分别为(0,1,0,1,0,…,0)和(0,1,0,0,1,0,…,0)的循环图的邻点可区别全色数.

For a connected graph G with an order no less than 2, the adjacent-vertex-distinguishing total coloring on it means that the color and color set of arbitrary two adjacent vertices on G is different and, furthermore,the color of arbitrary two adjacent sides with a vertex is different from that of their correlative sides as well. The adjacent-vertex-distinguishing total chromatic numbers on cyclic graphs are given in the form of the elements of first row （0,1,0,1,0,…, 0） and （0,1,0,0,1,0, …, 0） in two classes of adjacent matrixes, respectively.