梯图的点可区别全染色(n≡5(mod8))

Vertex-distinguishingtotal coloring of ladder graphs(n≡5(mod8))

一个图的全染色被称为点可区别的即对任意两个不同点的相关联元素及其本身所构成的色集合不同。其中所用的最少颜色数称为G的点可区别全色数。本文定义了一种排序方法:三角排序。利用该排序的结果证明了当n≡5(mod8)和C4n-1/2+2<m≤C4n/2+2时,梯图Lm≌Pm×P2的点可区别全色数为n。

A proper total coloring of a simple graph G is called vertex distinguishing if for any two distinct vertices u and v in G, the set of colors assigned to the elements incident and itself to u differs from the set of colors incident to v. The minimal number of colors required for a vertex distinguishing total coloring of G is called the vertex distingguishing total coloring chromatic number. In this paper, we give a ＂triangle compositor＂, by the compositor, we proved that when n≡5（mod8） and C4n-1/2＋2m≤C4n/2＋2, vertex distinguishing total chromatic number of ＂ladder graphs＂ Lm is n.