| Hamilton图的充要条件及圈的矩阵算法 |
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| 引用本文： | 张国志,王世英.Hamilton图的充要条件及圈的矩阵算法[J].山西大学学报(自然科学版),2006,29(3):239-241. |
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| 作者姓名： | 张国志 王世英 |
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| 作者单位： | 1. 晋中学院,数学系,山西,晋中,030600
2. 山西大学,数学科学学院,山西,太原,030006 |
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| 基金项目： | 山西省自然科学基金;国家自然科学基金 |
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| 摘 要： | 利用矩阵方法得到了一个简单无向图为H am ilton图的充要条件等一些结论以及圈的矩阵算法.一个n阶简单无向图是H am ilton图的充要条件是其n阶长路矩阵是一个对角线元素全不为0的对角阵,且对角线上每一个元素均为H am ilton圈之和.
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| 关 键 词： | 路矩阵 k阶长路矩阵 Hamilton图 圈 |
| 文章编号： | 0253-2395(2006)03-0239-03 |
| 收稿时间： | 2005-03-01 |
| 修稿时间： | 2005年3月1日 |
The Necessary and Sufficient Conditions for the Hamilton Graph and Matrix Calculation of Cyles |
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| ZHANG Guo-zhi,WANG Shi-ying.The Necessary and Sufficient Conditions for the Hamilton Graph and Matrix Calculation of Cyles[J].Journal of Shanxi University (Natural Science Edition),2006,29(3):239-241. |
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| Authors: | ZHANG Guo-zhi WANG Shi-ying |
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| Institution: | 1. Department of Mathematics ,Jinzhong University ,Jinzhong ,Shanaci 030600 ,China ; 2. School of Mathematical Sciences ,Shanaci University, Taiyuan 030006 ,China |
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| Abstract: | The necessary and sufficient conditions for a simple undirected graph to be a Hamilton graph and relevant results with matrix algorithm of cycles are obtained by using the matrix approaches.For example,a simple undirected graph of order n is a Hamilton graph if and only if it's path matrix of order n is a diagonal matrix that none of elements of diagonal line is zero,and each element of diagonal line is the sum of Hamilton cycles. |
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| Keywords: | path matrix path matrix of order k Hamilton graph cycle |
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