一些图的Mycielski图的均匀全色数

Equitable Total Chromatic Numbers of Mycielski Graphs of Some Graphs

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.