| 单圈图的无符号狄利克雷谱半径 |
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| 引用本文： | 张光军,李伟霞. 单圈图的无符号狄利克雷谱半径[J]. 数学研究及应用, 2017, 37(3): 262-266 |
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| 作者姓名： | 张光军 李伟霞 |
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| 作者单位： | 青岛科技大学数理学院, 山东 青岛 266061,青岛大学数学与统计学院, 山东 青岛 266071 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11271256; 11601208). |
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| 摘 要： | Let G be a simple connected graph with pendant vertex set ?V and nonpendant vertex set V_0. The signless Laplacian matrix of G is denoted by Q(G). The signless Dirichlet eigenvalue is a real number λ such that there exists a function f ≠ 0 on V(G) such that Q(G)f(u) = λf(u) for u ∈ V_0 and f(u) = 0 for u ∈ ?V. The signless Dirichlet spectral radiusλ(G) is the largest signless Dirichlet eigenvalue. In this paper, the unicyclic graphs with the largest signless Dirichlet spectral radius among all unicyclic graphs with a given degree sequence are characterized.
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| 关 键 词： | 无符号狄利克雷谱半径 单圈图 度序列 |
| 收稿时间： | 2016-01-20 |
| 修稿时间： | 2017-02-27 |
The Signless Dirichlet Spectral Radius of Unicyclic Graphs |
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| Guangjun ZHANG and Weixia LI. The Signless Dirichlet Spectral Radius of Unicyclic Graphs[J]. Journal of Mathematical Research with Applications, 2017, 37(3): 262-266 |
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| Authors: | Guangjun ZHANG and Weixia LI |
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| Affiliation: | School of Mathematics and Physics, Qingdao University of Science and Technology, Shandong 266061, P. R. China and School of Mathematics and Statistics, Qingdao University, Shandong 266071, P. R. China |
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| Abstract: | Let $G$ be a simple connected graph with pendant vertex set $partial V$ and nonpendant vertex set $V_0$. The signless Laplacian matrix of $G$ is denoted by $Q(G)$. The signless Dirichlet eigenvalue is a real number $lambda$ such that there exists a function $f neq 0$ on $V(G)$ such that $Q(G)f(u)=lambda f(u)$ for $u in V_0$ and $f(u)=0$ for $u in partial V$. The signless Dirichlet spectral radius $lambda(G)$ is the largest signless Dirichlet eigenvalue. In this paper, the unicyclic graphs with the largest signless Dirichlet spectral radius among all unicyclic graphs with a given degree sequence are characterized. |
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| Keywords: | signless Dirichlet spectral radius unicyclic graph degree sequence |
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