几类特殊Corona图的b-染色数与b-连续性研究  

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

作　　者：吕闯[1] 张若东[1] 潘淑霞[1] LV Chuang ZHANG Ruo-dong PAN Shu-xia(Shcool of Public Health, Jilin Medical University, Jilin 132013, China)

机构地区：[1]吉林医药学院公共卫生学院,吉林132013

出　　处：《数学的实践与认识》2017年第5期147-157,共11页Mathematics in Practice and Theory

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=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.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 Pn·Pm,Pn·K（1,m） and Pn · W（m＋1）.

关 键 词：b-染色 b-染色数 b-连续 m-度 Corona图 

分 类 号：O157.5[理学—数学]