一些图的Mycielski图的均匀全色数  

Equitable Total Chromatic Numbers of Mycielski Graphs of Some Graphs

作　　者：郭丽娜[1] 马刚[2] GUO Lina MA Gang(College of Preparatory Education College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, China)

机构地区：[1]西北民族大学预科教育学院,甘肃兰州730030 [2]西北民族大学数学与计算机科学学院,甘肃兰州730030

出　　处：《济南大学学报（自然科学版）》2017年第2期176-180,共5页Journal of University of Jinan(Science and Technology)

基　　金：甘肃省自然科学基金项目(145RJZA158);西北民族大学中央高校基本科研业务费专项资金(ZYZ2011082)

摘　　要：采用构造法和加点加边法,并借助均匀边染色理论,研究一些图的Mycielski图的均匀全染色问题,给出路、圈、星、扇、轮的Mycielski图的均匀全色数。结果表明,在路、圈、星、扇、轮的Mycielski图M(P_n)、M(C_n)、M(S_n)、M(F_n)、M(W_n)中,M(P_2)、M(S_1)的均匀全色数均为Δ+2,其余图的均匀全色数均为Δ+1,其中n为自然数,Δ为图的最大度数。The problem of equitable total coloring on Mycielski graphs of some graphs was researched by using the methods of construction and adding vertices edge with the help of equitable edge coloring theory. The equitable total chromatic numbers of Mycielski graphs such as path, cycle, star, fan and wheel were given. The results show that among the Mycielski graphs such as path, cycle, star, fan, and wheel ofM（Pn） , M（Cn）, M（Sn）, M（Fn）, and M（Wn）, both of the equitable total chromatic numbers of M（P2 ） and M（ S1 ） are△＋2, and the equitable total chromatic numbers of the left graphs are△＋1, where n is a natural number and△ is the maximum degree of graph.

关 键 词：图 MYCIELSKI图 均匀全染色 均匀全色数 

分 类 号：O157.5[理学—数学]