【摘要】 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=G₁·G₂为图G₁与G₂的Corona图,其中G包含G₁的一个拷贝,包含G₂的|V（G₁）|个拷贝,且G₁的第i个顶点与G₂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.更多还原

【Abstract】 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（χ（G） ≤ k ≤ b（G））colors.The Corona graph of two graphs G₁and G₂ is the graph G = G₁ · G₂ formed from one copy of G₁ and |V（G₁）| copies of G₂where 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 P_n·P_m,P_n·K_1,m and P_n · W_m+1.更多还原