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中文摘要：
本文研究了最大度为3且没有相邻最大度的图的邻点可区别全染色．利用边剖分的方法，构造了此类图更为一般的情形，得到了它们的邻点可区别全色数的上界．目前，未找到最大度为3的图且它的邻点可区别全色数是6．本文的结果部分地回答了这个问题．
英文摘要：
In this paper, we study the adjacent vertex distinguishing total colorings of graphs with maximum degree three and no adjacent A-vertices. By the technique of splitting edges, graphs with more special situations are constructed. And then we obtain the upper bound of adjacent vertex distinguishing total chromatic numbers of these graphs. Up to present graph having maximum degree three such that its adjacent vertex distinguishing total chromatic number is six has been reported in current literature, our conclusion answers this problem partially.
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