几类特殊Corona图的b-染色数与b-连续性研究

在一个图G的正常k染色中,如果每一个颜色类中都至少存在一个顶点,使得其在其它的k-1个颜色类中都至少有一个邻居,则称这样的正常k染色为b-染色.一个图G的b-染色数是最大的正整数k,使得用k种颜色能够对G进行b-染色,用b(G)来表示.如果对于任意的正整数k:χ(G)≤k≤b(G),用k种颜色可以对图G进行b-染色,则称图G是b-连续的.设G1与G2为任意图,称图G=G_1·G_2为图G_1与G_2的Corona图,其中G包含G_1的一个拷贝,包含G_2的|V(G_1)|个拷贝,且G_1的第i个顶点与G_2的第i个拷贝的所有顶点都邻接.研究了路图与路图、星形图以及轮图所构成的Corona图P_n·P_m、P_n·K_(1,m)以及P_n·W_(m+1)的m-度,b-染色数与b-连续性.

On The b-Chromatic Number and b-Continuity of Some Special Corona Graphs

A (k)b-coloring of G is a proper coloring of the vertices of a graph G such that there exists a vertex in each color class joined to at least one vertex in each other color class.The b-chromatic number of a graph G is the maximum integer k such that G has a b-coloring with k colors,denoted by b(G).A graph G is defined to be b-continuous if it admits a b-coloring with k(x(G) ≤ k ≤ b(G))colors.The Corona graph of two graphs G1 and G2 is the graph G =G1 ο G2 formed from one copy of G1 and |V(G1)| copies of G2 where the ith vertex of G1 is adjacent to every vertex in the ith copy of G2.The b-chromatic number m-degree and the b-continuous of some special Corona graphs are studied,Which including Pn ο Pm,Pn ο K1,m and Pn ο Wm+1.