| 两类广义Petersen 图的Euler亏格 |
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| 引用本文： | 马登举,任韩,卢俊杰.两类广义Petersen 图的Euler亏格[J].数学物理学报(A辑),2009,29(1):25-31. |
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| 作者姓名： | 马登举 任韩 卢俊杰 |
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| 作者单位： | 马登举,Ma Dengju(华东师范大学数学系,上海 200062;南通大学理学院,江苏南通 226007);任韩,Ren Han(华东师范大学数学系,上海,200062);卢俊杰,Lu Junjie(华东理工大学数学系,上海,200240)
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| 基金项目： | 国家自然科学基金，上海市科委重点基金 |
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| 摘 要： | 广义 Petersen 图 P(n, m) 是这样的一个图:它的顶点集是{ui, vi | i=0,1, … , n-1}, 边集是 {uiui+1, vivi+m, uivi | i=0,1, …, n-1}, 这里 m, n 是正整数、加法是在模n 下且 m<|n/2| . 这篇文章证明了P(2m+1, m)(m≥ 2) 的 Euler 亏格是1, 并且 P(2m+2, m)(m≥ 5) 的 Euler 亏格是2.
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| 关 键 词： | 胞腔嵌入 Euler 亏格 广义 Petersen图. |
| 收稿时间： | 2006-03-10 |
| 修稿时间： | 2008-10-09 |
The Euler Genera of Two Classes of Generalized Petersen Graphs |
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| Ma Dengju,Ren Han,Lu Junjie.The Euler Genera of Two Classes of Generalized Petersen Graphs[J].Acta Mathematica Scientia,2009,29(1):25-31. |
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| Authors: | Ma Dengju Ren Han Lu Junjie |
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| Institution: | (1.Department of Mathematics, East China Normal University, Shanghai 200062; 2. School of Science, Nantong University, Jiangsu Nantong 226007;
3. Department of Mathematics, East China University of Science and Technology, Shanghai 200210) |
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| Abstract: | The generalized Petersen graph P(n, m) is such a graph that its vertex set is {ui, vi |i=0,1, …, n-1} and edge set is {uiui+1, vivi+m, uivi | i=0,1, …, n-1}, where m, n are positive integers satisfying m< |n/2| and indices is read modulo n. It is proved that the Euler genus of P(2m+1, m)(m≥2) is 1 and that the Euler genus of P(2m+2, m)(m≥5) is 2. |
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| Keywords: | Cellular embeddingzz Euler genuszz Generalized Petersen graph zz |
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