| Equitable Total Coloring of Some Join Graphs |
| Received:November 13, 2006 Revised:March 23, 2007 |
| Key Words:
equitable total coloring equitable total chromatic number join graph equitable edge coloring.
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| Fund Project:the National Natural Science Foundation of China (No.10771091). |
| Author Name | Affiliation | | GONG Kun | Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
Graduate School of the Chinese Academy of Sciences, Beijing 100080, China | | ZHANG Zhong Fu | Institute of Applied Mathematics, Lanzhou Jiaotong University, Gansu 730070, China
Department of Applied Mathematics, Northwest Normal University, Gansu 730070, China | | WANG Jian Fang | Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
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| Abstract: |
| 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 $m \geq n \geq 3$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.04.010 |
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