| Hamilton图的一个充要条件 |
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| 引用本文： | 刘永平,谢继国.Hamilton图的一个充要条件[J].甘肃科学学报,2004,16(3):20-22. |
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| 作者姓名： | 刘永平 谢继国 |
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| 作者单位： | 兰州师范高等专科学校数学系,甘肃,兰州,730070 |
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| 摘 要： | 通过对图的关联矩阵与回路矩阵的正交性讨论，得出用基底关联矩阵A=(A11 A12)计算基本回路矩阵Bf的公式Bf=(U A11^T(A12^-1)^T)；根据计算出的基本回路矩阵Bf的特征，得到一个判定Hamilton图的充要条件——图的基本回路矩阵中必有一行有且仅有n个非零元素(n为图的顶点数)．
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| 关 键 词： | 回路矩阵 关联矩阵 正交性 Hamilton图 充要条件 |
| 文章编号： | 1004-0366(2004)03-0020-03 |
| 修稿时间： | 2004年4月7日 |
A Sufficient and Necessary Condition for Hmilton Graph |
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| LIU Yong-ping,XIE Ji-guo.A Sufficient and Necessary Condition for Hmilton Graph[J].Journal of Gansu Sciences,2004,16(3):20-22. |
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| Authors: | LIU Yong-ping XIE Ji-guo |
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| Abstract: | Through the discussion of orthogonality for loop matrix and incidence matrix of the graph, a calculation formula B_f=(UA~T_(11)(A~(-1)_(12))~T) of fundermental loop matrix B_f was obtained, using the basis incidence matrix A=(A_(11)A_(12)). A sufficient and necessary condition of Hamilton graph is achieaed according to the feature of fundermental loop matrix B_f calculated-the fundermental loop matrix must have a line that has and has only n elements which are not equal to 0 (n is the vertex number of the graph). |
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| Keywords: | loop matrix incidence matrix orthogonality Hamilton graph sufficient and necessary condition |
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