中文摘要：

应用构造染色函数法研究了冠图Cm·Pn、Pm·Cn的邻点可区别V-全染色．通过对Pm·Cn的邻点可区别V-全染色的研究巧妙给出了Cm·Cn邻点可区别V-全染色，并得到了这些图的邻点可区别V-全色数，从而验证了图的邻点可区别V-全染色猜想．

英文摘要：

In this paper, the adjacent vertex-distinguishing V-total coloring of Cm· Pn and Pm· Cn are obtained by constructing coloring function. Through the adjacent vertex- distinguishing V-total coloring of Pm· Cn, we skilfully get the adjacent vertex-distinguishing V-total coloring of Cm· Cn, and obtain the adjacent vertex-distinguishing V-total chromatic number of those graphs. Further, the conjecture of adjacent vertex-distinguishing V-total coloring of graphs is checked.