几类Corona图的b-染色数

The b-chromatic Number of Some Corona Graphs

设{V_1,V_2,···,V_k}为图G=(V,E)的一个正常顶点染色,满足对任意的i,j:1≤i≠j≤k,存在于u∈V_i,v∈V_j,使得uv∈E,称该点染色为G的一个b-染色.一个图G的b-染色数是最大的整数k,满足用k种颜色能对G进行b-染色,用b(G)来表示.如果对任意的k:χ(G)≤k≤b(G),图G都存在一个(k)b-染色{V_1,V_2,···,V_k},称G是b-连续的.根据Corona图的结构特点,设计循环染色方案,通过对Corona图中两种类型的顶点进行循环染色,得出几类Corona图的b-染色数等于其m-度,且这些Corona图满足b-连续性.

Let{V1;V2;···;Vk}be a proper vertex coloring of a graph G=(V;E),which is called a b-coloring of G,if for all i;j:1≤i?=j≤k,exists u∈Vi;v∈Vj,satisfying uv∈E.The maximum positive integer k for a b-coloring{V1;V2;···;Vk}on a graph G is called the b-chromatic number,denoted by b(G).A graph G is called b-continuity if for all k: (G)≤k≤b(G),there exists a(k)b-coloring on graph G.According to the structural char-acteristics of the Corona graphs,the cyclic coloring schemes are constructed.Through the cyclic coloring on two kinds of vertices of Corona graphs,the b-chromatic number of several Corona graphs equalling to its m-degree is obtained,and all these Corona graphs are b-continuous.