中文摘要：

对简单图G（V,E）,存在一个正整数k,使得映射f：V（G）∪E（G）→{1,2,…,k},如果 uv∈E（G）,有f（u）≠f（v）,f（u）≠f（uv）且C（u）≠C（v）,其中：C（u）={f（u）}∪{f（uv）,f（v）｜uv∈E（G）,v∈V（G）},则称f是图G的邻点强可区别E-全染色,且称最小的数k为图G的邻点强可区别E-全色数.本文应用构造染色法研究了有关路的平方及立方图的邻点强可区别E-全染色,并得出其邻点强可区别E-全色数.

英文摘要：

Let G（V,E） be a simple graph,and k be a positive integer,f is a mapping from V（G）∪E（G） to {1,2,… ,k} ,then it is called the adjacent vertex strongly distinguishing E-total coloring of G. if uvE∈（G） ,f（u）≠f（v） ,f（u）≠f（uv） ,C（u）≠C（v）, where C（u） is {f（u） }∪ {f（uv） ,f （v）[uv∈ E（G）,v∈V（G）}, and the minimum number of k is called the adjacent vertex strongly distinguishing E-total chromatic of G. The structure staining method is used to study the adjacent vertex strongly distinguishing E-total coloring of graph of square and cube of path on this basis. And the adjacent vertex strongly distinguishing E-total chromatic of graph of square and cube of path is obtained thereby.