The Spectral Radius and the Maximum Degree of Irregular Graphs
The Spectral Radius and the Maximum Degree of Irregular Graphs
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DOI：
10.37236/956
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发表时间：
2007-02
期刊：
影响因子：
--
通讯作者：
S. Cioabă
中科院分区：
文献类型：
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作者：
S. Cioabă
设$G$是一个顶点数为$n$的最大度为$\Delta$，直径为$D$的非正则图。我们证明了$$ \Delta-\Delta_1>{1\over nD}，$$其中$\Delta_1 $是$G$的邻接矩阵的最大特征值。我们还研究了添加或删除几个边对正则图的谱半径的影响。
Let $G$ be an irregular graph on $n$ vertices with maximum degree $\Delta$ and diameter $D$. We show that $$ \Delta-\lambda_1>{1\over nD}, $$ where $\lambda_1$ is the largest eigenvalue of the adjacency matrix of $G$. We also study the effect of adding or removing few edges on the spectral radius of a regular graph.