| 关于k-优美图一个猜想的证明 |
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| 引用本文： | 李武装,严谦泰.关于k-优美图一个猜想的证明[J].河南科技大学学报(自然科学版),2011,32(5):81-84,1. |
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| 作者姓名： | 李武装 严谦泰 |
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| 作者单位： | 安阳师范学院公共计算机教学部,河南安阳,455002 |
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| 基金项目： | 河南省自然科学基金项目(0511013800) |
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| 摘 要： | 二分图是一类有着广泛应用的图,但这类图并不都是优美图,因此需要进一步深入研究它的优美性。本文根据马克杰教授提出的猜想:完备二分图Km,n的冠是k-优美图(m≤n,k≥2),利用构造法证明了当m=1或m=2,k≥2时,猜想成立;当m≥3,k≥(m-2)(n-1)时,猜想成立。拓展了k-优美性的研究范围。
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| 关 键 词： | 完备二分图 冠 k-优美值 k-优美图 |
A Proof of a Conjecture About k-graceful Graph |
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| LI Wu-Zhuang,YAN Qian-Tai.A Proof of a Conjecture About k-graceful Graph[J].Journal of Henan University of Science & Technology:Natural Science,2011,32(5):81-84,1. |
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| Authors: | LI Wu-Zhuang YAN Qian-Tai |
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| Institution: | LI Wu-Zhuang,YAN Qian-Tai(Teaching Department of Computer,Anyang Normal University,Anyang 455002,China) |
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| Abstract: | Bipartite graphs are widely applied,but not all bipartite graphs are graceful graphs.Therefore,it is necessary to research their gracefulness further.Based on the conjecture put forwarded by professor Ma Kejie that crown of complete bipartite graphs is k-graceful(m≤n,k≥2),the conjecture is proved by construction method when(m=1or 2,k≥2);(m≥3,k≥(m-2)(n-1)) in the paper.The k-graceful research rang is extended. |
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| Keywords: | Complete bipartite graphs Crown k-graceful value k-graceful graphs |
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