| Vertex Distinguishing Equitable Total Chromatic Number of Join Graph |
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| 作者姓名： | Zhi-wen Wang Li-hong Yan Zhong-fuZhang |
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| 作者单位： | [1]Department of Mathematics of Yeungnam University, Daedong, Kyongsan, Kyongbuk 712-749, Korea [2]Department of Mathematics of Xianyang Normal University, Xianyang 712000, China [3]School of Mathematics of Lanzhou Jiaotong University, Lanzhou 730070, China |
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| 基金项目： | Supported by the Xianyang Normal University Foundation for Basic Research （No.06XSYK266） and Com2MaC- K0SEF（R11-1999-054）.Acknowledgements. We are grateful to an anonymous referee for many remarks and suggestions which led to substantial improvement in the presentation of this work. |
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| 摘 要： | A vertex distinguishing equitable total coloring of graph G is a proper total coloring of graph G such that any two distinct vertices＇ coloring sets are not identical and the difference of the elements colored by any two colors is not more than 1. In this paper we shall give vertex distinguishing equitable total chromatic number of join graphs Pn VPn, Cn VCn and prove that they satisfy conjecture 3, namely, the chromatic numbers of vertex distinguishing total and vertex distinguishing equitable total are the same for join graphs Pn V Pn and Cn ∨ Cn.
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| 关 键 词： | 图论 路径 合理估计 数学 |
| 收稿时间： | 11 December 2005 |
| 修稿时间： | 2005-12-112007-03-26 |
Vertex Distinguishing Equitable Total Chromatic Number of Join Graph |
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| Zhi-wen Wang Li-hong Yan Zhong-fuZhang.Vertex Distinguishing Equitable Total Chromatic Number of Join Graph[J].Acta Mathematicae Applicatae Sinica,2007,23(3):433-438. |
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| Authors: | Zhi-wen Wang Li-hong Yan Zhong-fu Zhang |
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| Institution: | (1) Department of Mathematics of Yeungnam, University, Daedong, Kyongsan, Kyongbuk, 712-749, Korea;(2) Department of Mathematics of Xianyang Normal University, Xianyang, 712000, China;(3) School of Mathematics of Lanzhou Jiaotong University, Lanzhou, 730070, China |
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| Abstract: | Abstract
A vertex distinguishing equitable total coloring of graph G is a proper total coloring of graph G such that any two distinct vertices' coloring sets are not identical and the difference of the elements colored by any two
colors is not more than 1. In this paper we shall give vertex distinguishing equitable total chromatic number of join graphs
P
n
∨P
n
,Cn∨C
n
and prove that they satisfy conjecture 3, namely, the chromatic numbers of vertex distinguishing total and vertex distinguishing
equitable total are the same for join graphs P
n
∨P
n
and Cn∨C
n
.
Supported by the Xianyang Normal University Foundation for Basic Research (No.06XSYK266) and Com2MaC-KOSEF( R11-1999-054). |
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| Keywords: | Path cycle join graph vertex distinguishing equitable total chromatic number |
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