| 给定顶点数和边数的连通图的Q-谱半径的界 |
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| 引用本文： | 陈琳,黄琼湘.给定顶点数和边数的连通图的Q-谱半径的界[J].运筹学学报,2011,15(3):19-28. |
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| 作者姓名： | 陈琳 黄琼湘 |
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| 作者单位： | 1. 新疆医科大学医学工程技术学院数学教研室;
2.新疆大学数学与系统科学学院 |
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| 基金项目： | the National Natural Science Foundation of China(10961023) |
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| 摘 要： | 图的无符号拉普拉斯矩阵是图的邻接矩阵和度对角矩阵的和,其特征值记为q1≥q2≥…≥qn.设C(n,m)是由n个顶点m条边的连通图构成的集合,这里1≤n-1≤m≤(n2).如果对于任意的G∈C(n,m)都有q1(G*)≥q1(G)成立,图G*∈C(n,m)叫做最大图.这篇文章证明了对任意给定的正整数a=m-n+1,如果n...
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| 关 键 词： | 无符号拉普拉斯矩阵 最大图 嵌套分裂图 Q-谱半径 |
| 收稿时间： | 2011-02-09 |
| 修稿时间： | 2011-05-16 |
The Bound of Q-Spectral Radii of Connected Graphs with Given Number of Vertices and Edges |
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| CHEN Lin,HUANG Qiongxiang.The Bound of Q-Spectral Radii of Connected Graphs with Given Number of Vertices and Edges[J].OR Transactions,2011,15(3):19-28. |
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| Authors: | CHEN Lin HUANG Qiongxiang |
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| Affiliation: | CHEN Lin HUANG Qiongxiang 1.College of Medical Engineering and Technology,Xinjiang Medical University,Urumqi 830011,China,2.College of Mathematics and System Science,Xinjiang University,Urumqi 830046 |
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| Abstract: | The signless Laplacian matrix of a graph is defined to be the sum of its adjacency matrix and degree diagonal matrix,and its eigenvalues are denoted by q1 ≥q2 ≥ … ≥ qn.Let C(n,m) be a set of connected graphs in which every graph has n vertices and m edges,where 1 ≤ n - 1 ≤ m ≤ (n2).A graph G* ∈ C(n,m) is called maximum if q1(G*) ≥ q1(G) for any G ∈ C(n,m).In this paper,we proved that for any given positive integer a=m-n+1,n ＜ q1(G*) ＜ n+1 if n＞-1/2+a+1/2√(1+12a+12a2),which leads to q1(G) ＜ n + 1 for any G ∈ C(n,m) whenever n ＞ -1/2 + a + 1/2√(1 + 12a + 12a2). |
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| Keywords: | signless Laplacian maximum graph nested split graph Q-spectral radius |
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