中文摘要：

图的正常k-全染色是用k种颜色给图的顶点和边同时进行染色，使得相邻或者相关联的元素（顶点或边）染不同的染色．使得图G存在正常k-全染色的最小正整数惫，称为图G的全色数，用χ″（G）表示．证明了若图G是最大度△≥6且不含5-圈和相邻6-圈的平面图，则χ″（G）=△＋1．

英文摘要：

A proper k-total-coloring of a graph G is a coloring of V（G） ∪ E（G） using k-colors such that no two adjacent or incident elements receive the same color.The total chromatic number χ″ （G） of G is the smallest integer such that G has a k-total-coloring.It＇s proved that if G is a planar gragh with maximum degree at least 6 and without 5-cycles and intersecting 6-cycles,then χ″（G）=△＋1.