若干图的点强全着色

图G(V,E)的一正常k-全着色σ称为G(V,E)的一个k-点强全着色,当且仅当v∈V(G),N[v]中的元素着不同颜色,其中N[v]={u|vu∈E(G)}∪{v}.并且vχsT(G)=min{k|存在G的一个k-点强全着色}称为G(V,E)的点强全色数.本文得到了一些特殊图的点强全色数χvTs(G),并提出猜想:对于简单图G,有k(G)≤χvTs(G)≤k(G)+1,这里k(G)表示图G中所有顶点间距离不超过2的点集的最大顶点数.

The Vertex Strong Total Coloring of Some Graphs

A proper k-total coloring σ of graph G(V,E) is called a k-vertex strong total coloring of G(V,E) if and only if for v∈V(G),the elements in N[v] are colored with different colors,where N[v]={u|vu∈E(G)}∪{v};and χvsT(G)=min{k|there is a k-vertex strong total coloring of G} is called the vertex strong total chromatic number of G.In this paper,we obtain the vertex strong total chromatic number χvsT(G) of some special graphs and present a conjecture: For simple graph G,has k(G)≤χvsT(G)≤k(G)+1,where k(G) denotes the maximum value of the element of all such vertices set where the distance between each two vertices is at most 2.