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| 连通图的度序列及连通平面图的低度点个数 | |
| 引用本文： | 赵衍才,张裕生,苗连英.连通图的度序列及连通平面图的低度点个数[J].大学数学,2009,25(2). |
| 作者姓名： | 赵衍才 张裕生 苗连英 |
| 作者单位： | 1. 蚌埠学院,理学系,安徽,蚌埠,233030 2. 蚌埠学院,科技处,安徽,蚌埠,233030 3. 中国矿业大学,理学院,江苏,徐州,221008 |
| 摘 要： | 美国数学家Bondy给出了一个非负整数序列为简单图的度序列的充要条件.本文对此进行了发展,证明了一个正整数序列为连通简单图的度序列的充要条件;然后在此基础上又探讨了平面图的低度点个数问题并定义了描述连通平面图的低度点个数的一个概念φ(n,m),并对某些低阶平面图求出了φ(n,m)的值.最后给出了φ(n,m)的上下界. |
| 关 键 词： | 平面图 度序列 图序列 φ(n m) |
The Degree Sequence of Connected Graphs and the Number of Lower Degree Vertices of Connected Plannar Graphs |
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| ZHAO Yan-cai,ZHANG Yu-sheng,MIAO Lian-ying.The Degree Sequence of Connected Graphs and the Number of Lower Degree Vertices of Connected Plannar Graphs[J].College Mathematics,2009,25(2). | |
| Authors: | ZHAO Yan-cai ZHANG Yu-sheng MIAO Lian-ying |
| Institution: | 1.Department of Mathematics;Bengbu College;Bengbu;Anhui 233030;China;2.Division of Science and Technology;3.Science College;China University of Mining and Technology;Xuzhou;Jiangsu 221008;China |
| Abstract: | The necessary and sufficient condition on which a degree sequence is a graph sequences is given by American mathematician Bondy.In this paper,after proving a necessary and sufficient condition on which a degree sequence is a sequence of connected graph,we gave a conception φ(n,m) which denotes the number of lower degree vertices of connected planar graphs,and for some small values of n,we obtained the corresponding φ(n,m).At last, we gave an upper and lower bound of φ(n,m). |
| Keywords: | planar graph degree sequence graph sequence φ(n m) |
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