两类广义Petersen图的点可约边(全)染色

Vertex Reducible Edge (Total) Coloring of Two Classes of Generalized Petersen Graph

图G的一个(非正常)边(全)染色f满足任意两个顶点的度相同时色集合相同,则称f是图G的一个点可约边(全)染色,其中任一点的色集合为该点(或该点及其)关联边所分配的颜色构成的集合,将所用的最多颜色数称为图G的点可约边(全)色数。运用组合分析法和构造染色函数法得到了广义Petersen图P(n,1)和P(n,2)的点可约边(全)色数。

A non-proper edge (total) coloring f of G such that any two vertices with the same degree have the same color sets is called a vertex-reducible edge (total) coloring fof G, where the color set of each vertex consists of all colors assigned to (or thevertex and) its incident edges, and the maximum number the color required is saidvertex reducible edge (total) chromatic number. In this paper, the vertex reducibleedge (total) chromatic number of generalized Petersen graphs P(n,1) and P(n,2) areobtained by combination analysis and construction coloring function.