星和轮的Mycielski图的[r,s,t]色数

给定非负整数r,s和t,若图G(V,E)有一个映射σ:V∪E→{0,1,…,k-1},k∈N,满足对V中相邻的点v_i,v_j有|σ(v_i)-σ(v_j)|≥r;对E中相邻的边e_i,e_j有|σ(e_i)-σ(e_j)|≥s;对V∪E中相关联的点v_i和边e_j有|σ(v_i)-σ(e_j)|≥t,则称σ为G的一个r,s,t]-着色.使得图G存在使用了k种颜色的r,s,t]-着色的最小整数k称为G的r,s,t]-色数.研究星和轮的Mycielski图的r,s,t]-着色,并给出其在一定条件下的r,s,t]-色数.

The[r,s,t]Chromatic Number of Mycielski Graph of Star and Wheel

Given non- negative integers r,s,and t,anr,s,t]-coloring of a graph G =(V,E)is a mapping σ from V∪E to the color set {0,1,2,…,k- 1} such that |σ(v_i)--σ(v_j)|≥ r for every two adjacent vertices v_i,v_j,|σ(e_i)-σ(e_j)| > s for every two adjacent edge e_i,e_j,and |σ{vi) —σ(e_j)| ≥ t for all pairs of incident vertices and edges,respectively.Ther,s,t]-chromatic number χ_(r,s,t)(G) of G is defined to be the minimum A;such that G admits anr,s,t]-coloring using k colors.This paper give ther,s,t]-chromatic number of Mycielski graph of star and wheel if r,s,t meet certain conditions.