| For a graph G, we assign a color on its every vertex and every edge. If: (1) for any two adjacent vertices,two adjacent edges and any pair of incident vetex and egde, we receive different colors; (2) the color sets of vertices which consist of the colors on every vertex and edges incident with the vertex are pairwise distinct, then we call this assignment vertex distinguishing total coloring of G. The minimum color number of vertex distinguishing total coloring of G is called the vertex distinguishing total chromatic number of G, denoted by xvt (G) . In this paper, we obtain a new sequence of all combinations of 4 elements selected from the set {1,2,...,n) by changing some combination positions appropriately on the lexicographical sequence. We call it the new triangle sequence. Using this technique, we obtain vertex distinguishing total chromatic number of ladder graphs Lm (?) Pm×P2 as follows:(1) For ladder graphs Lm (4≤m< 250), we have(2) For any integer n = 10 + 8k(k = 1,2,…) and , wehave... |
