| 双圈图的零度与其匹配数之间的关系 |
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| 引用本文： | 萨如拉,长安,李建喜.双圈图的零度与其匹配数之间的关系[J].数学研究及应用,2016,36(6):631-643. |
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| 作者姓名： | 萨如拉 长安 李建喜 |
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| 作者单位： | 内蒙古农业大学理学院, 内蒙古 呼和浩特 010018,福州大学离散数学与理论计算机科学研究中心, 福建 福州 3510001,漳州师范学院数学与信息科学系, 福建 漳州 363000 |
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| 基金项目： | 国家自然科学基金 (Grant Nos.11331003; 11471077). |
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| 摘 要： | Let G be a graph with n(G) vertices and m(G) be its matching number.The nullity of G,denoted by η(G),is the multiplicity of the eigenvalue zero of adjacency matrix of G.It is well known that if G is a tree,then η(G) = n(G)-2m(G).Guo et al.Jiming GUO,Weigen YAN,Yeongnan YEH.On the nullity and the matching number of unicyclic graphs.Linear Alg.Appl.,2009,431:1293 1301]proved that if G is a unicyclic graph,then η(G)equals n(G)-2m(G)-1,n(G)-2m(G),or n(G)-2m(G) +2.In this paper,we prove that if G is a bicyclic graph,then η(G) equals n(G)-2m(G),n(G)-2m(G)±1,n(G)-2m(G)±2or n(G)-2m(G) + 4.We also give a characterization of these six types of bicyclic graphs corresponding to each nullity.
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| 关 键 词： | 零度 双圈图 匹配数 |
| 收稿时间： | 2015/10/10 0:00:00 |
| 修稿时间： | 2016/10/12 0:00:00 |
The Nullity of Bicyclic Graphs in Terms of Their Matching Number |
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| Rula SA,An CHANG and Jianxi LI.The Nullity of Bicyclic Graphs in Terms of Their Matching Number[J].Journal of Mathematical Research with Applications,2016,36(6):631-643. |
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| Authors: | Rula SA An CHANG and Jianxi LI |
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| Institution: | College of Science, Inner Mongolia Agricultural University, Inner Mongolia 010018, P. R. China,Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fujian 351000, P. R. China and Department of Mathematics and Information Science, Zhangzhou Normal University, Fujian 363000, P. R. China |
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| Abstract: | Let $G$ be a graph with $n(G)$ vertices and $m( G )$ be its matching number. The nullity of $G$, denoted by $\eta( G )$, is the multiplicity of the eigenvalue zero of adjacency matrix of $G$. It is well known that if $G$ is a tree, then $\eta( G )=n( G )-2 m( G )$. Guo et al. Jiming GUO, Weigen YAN, Yeongnan YEH. On the nullity and the matching number of unicyclic graphs. Linear Alg. Appl., 2009, 431: 1293--1301] proved that if $G$ is a unicyclic graph, then $\eta( G )$ equals $n( G ) - 2 m( G ) -1$, $n( G ) - 2 m( G ) $, or $n( G ) - 2 m( G ) +2$. In this paper, we prove that if $G$ is a bicyclic graph, then $\eta( G )$ equals $n( G ) - 2 m( G ) $, $n (G)-2m(G)\pm 1 $, $n( G ) - 2 m( G )\pm 2$ or $n( G ) - 2 m (G ) +4$. We also give a characterization of these six types of bicyclic graphs corresponding to each nullity. |
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| Keywords: | nullity bicyclic graphs matching number |
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