两类图的邻点强可区别E-全染色

On the Adaject Vertex Strong Distinguishing E-Total Coloring of Two Class Graph

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。本文在此基础上应用构造染色法研究了三正则图R(V,E)、强失积图P_mP_n的邻点强可区别E-全染色,并得出了其邻点强可区别E-全色数。

Let ） , （ E V G be a simple graph, k be a positive integer and f be a mapping from V（G）∪E（G）→{1 2…,k},, then it is called the adgacent vertex strongly distinguishing E-total coloring of G , if uv∈E（G）,f（u）≠f（v）,f（u）≠f（uv）C（u）≠C（v）, and the minimum number of k is called the adgacent vertex strongly distinguishing E-total chromatic of G . The paper applies the structure staining method to syudy the adjacent vertex strongly distinguishing E-total coloring of graph of 3-regular Rk,m and mn Pm Pn on this basis, and the adjacent vertex strongly distinguishing E-total chromatic of graph of 3-regular Rk,m and Pm Pn is obtained thereby.