关于图的点色数和邻点可区别E-全色数（英文）

On Chromatic Number and Adjacent Vertex-distinguishing E-total Chromatic Number of Graphs

图G的点色数χ(G)是指图G存在正常k-顶点着色的k的最小值,图G的邻点可区别E-全色数χe at(G)是指图G存在邻点可区别E-全染色的k的最小值.尽管图G的这两种染色看似不同,但我们证明:当χ(G)≥4时,χ(G)=χe at(G).

The chromatic number of a graphG, denoted byx（G）, is the minimum number k for which G has a proper k-vertex coloring. The adjacent vertex-distinguishing E-total chromatic number of G, denoted by χ（G）, is the minimum number k for which G has an adjacent vertex-distinguishing E-total coloring. These two colorings seem to be different, but we proved that X（G） =Xat（G） when x（G） t〉4.