| 最小Q-特征值为给定整数的一类图 |
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| 引用本文： | 沈富强,吴宝丰.最小Q-特征值为给定整数的一类图[J].上海理工大学学报,2014,36(5):425-428. |
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| 作者姓名： | 沈富强 吴宝丰 |
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| 作者单位： | 上海理工大学 理学院,上海,200093 |
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| 基金项目： | 国家自然科学基金资助项目(11301340,11201303,11101284);上海市自然科学基金资助项目(12ZR1420300) |
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| 摘 要： | 研究了基于二部图H构造的一类图的最小无符号拉普拉斯特征值,即最小Q-特征值,得到了它的最小Q-特征值的可达上界为1.给出了最小Q-特征值为1的2个必要条件,并构造了最小Q-特征值为1的一类图.另外,给出了利用H∨K1的最小Q-特征值来判断简单图H没有完美匹配的方法,以及图G增加边后最小Q-特征值保持不变的1个充分条件.最后,构造了最小Q-特征值为任意给定的正整数t的一类图.
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| 关 键 词： | 无符号拉普拉斯矩阵 最小Q-特征值 界 完美匹配 |
| 收稿时间： | 2013/8/16 0:00:00 |
A Class of Graphs with a Given Integer as Least Q-eigenvalue |
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| SHEN Fu-qiang and WU Bao-feng.A Class of Graphs with a Given Integer as Least Q-eigenvalue[J].Journal of University of Shanghai For Science and Technology,2014,36(5):425-428. |
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| Authors: | SHEN Fu-qiang and WU Bao-feng |
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| Institution: | College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China |
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| Abstract: | When H is a bipartite graph,the least signless Laplacian eigenvalue(the least Q-eigenvalue)of a class of graphs constructed by H was studied.It was shown that the sharp upper bound of the least Q-eigenvalue of the class of graphs is 1.Moreover,two necessary conditions were given for the graphs whose least Q-eigenvalue is equal to 1,and a class of graphs was constructed which have eigenvalue 1 as their least Q-eigenvalue.Also,a method was presented for checking a graph H without a perfect matching by using the least Q-eigenvalue of H∨K1,and a sufficient condition was given when adding edges without changing the least Q-eigenvalue.At last,a class of graphs were constructed which have least Q-eigenvalue t,where t is a given positive integer. |
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| Keywords: | signless Laplacian matrix least Q-eigenvalue bound perfect matching |
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