摘要
The total chromatic number χ T(G) of a graph G is the least number k such that G admits a total coloring with k colors. In this paper, it is proved that χ T(G)=Δ(G)+1 for all graphs with an unique major vertex of degree 4.
一个图Ｇ的全色数χＴ（Ｇ）是使得Ｖ（Ｇ）∪Ｅ（Ｇ）中相邻或相关联元素均染不同颜色的最少颜色数．文中证明了，若图Ｇ只有唯一的一个４度最大度点，则χＴ（Ｇ）＝Δ（Ｇ）＋１．
