部分图笛卡儿积图的邻点可区别VE-全染色

Adjacent vertex-distinguishing VE-total coloring of Cartesian product graph of some graphs

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},如果对uv∈E(G),有f(u)≠f(uv),f(v)≠f(uv),且C(u)≠C(v),则称f是图G的邻点可区别VE-全染色,且称最小的数k为图G的邻点可区别VE-全色数.讨论一些图的图笛卡儿积图的邻点可区别VE-全染色,得到它们的邻点可区别VE-全色数.

Let G（V,E） be a simple graph and k a positive integer.A mapping of f from V（G）∪E（G） to {1,2,…,k} was called the adjacent vertex-distinguishing VE-total coloring of G.If uv∈ E（G）,f（u）≠f（uv）,f（v）≠f（uv）,C（u）≠C（v）,where C（u）=f（u）∪f（uv）｜uv∈E（G）.The minimum number of k for which G had a AVD-VE-TC with k colors was called as adjacent vertex-distinguishing VE-total chromatic number of G.The adjacent vertex-distinguishing VE-total chromatic number of Cartesian product of some special graphs was discussed,so that their adjacent vertex-distinguishing VE-total chromatic numberwas obtained.