若干联图的均匀全染色

Equitable Total Coloring of Some Join Graphs

中文关键词:  均匀全染色  均匀全色数  联图  均匀边染色.

英文关键词:equitable total coloring  equitable total chromatic number  join graph  equitable edge coloring.

中文摘要:

      图$G(V,E)$的全色数 $\chi_{t}(G)$就是将$V\bigcup E$分成彼此不相交的全独立分割集的最小个数。 如果任何两个$V\bigcup E$的全独立分割集的元素数目相差不超过1，那么 $V \bigcup E$的全独立分割集的最小个数就称为图$G$的均匀全色数，记为$\chi_{et}(G)$。 在本文中我们给出了当 $m \geq n \geq 3$ 时 $W_m\bigvee K_n$，$F_m \bigvee K_n$及$S_m \bigvee K_n$ 的均匀全色数.

英文摘要:

      The total chromatic number $\chi_{t}(G)$ of a graph $G(V,E)$ is the minimum number of total independent partition sets of $V \bigcup E$, satisfying that any two sets have no common element. If the difference of the numbers of any two total independent partition sets of $V \bigcup E$ is no more than one, then the minimum number of total independent partition sets of $V \bigcup E$ is called the equitable total chromatic number of $G$, denoted by $\chi_{et}(G)$. In this paper, we have obtained the equitable total chromatic number of $W_m \bigvee K_n$, $F_m \bigvee K_n$ and $S_m \bigvee K_n$ while $m \geq n \geq 3$.