华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (4): 10-15.

• 应用数学与基础数学 • 上一篇    下一篇

图的能量的几个可达下界（英）

吴宝丰 1、2
袁西英 3
  

  1. 1.同济大学数学系,上海 200092; 2.上海理工大学理学院,上海 200093; 3.上海大学数学系,上海 200444
  • 收稿日期:2008-09-09 修回日期:2008-12-20 出版日期:2009-07-25 发布日期:2009-07-25
  • 通讯作者: 吴宝丰

Some sharp lower bounds for energy

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  1. 1. Department of Mathematics, Tongji University, Shanghai 200092, it China; 2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093 3. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • Received:2008-09-09 Revised:2008-12-20 Online:2009-07-25 Published:2009-07-25
  • Contact: WU Bao-feng

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摘要： 图\ $G$ 的能量\ $\mathcal{E}(G)$ 定义为它的邻接矩阵的所有特征值的绝对值之和,
在化学中, 它用来近似分子的\ $\pi$ 电子总能量. 本文给出了关于图的能量\ $\mathcal{E}(G)$
的几个下界, 同时刻画了达到这些下界的极图.

关键词: 图, 能量, 下界, 插值, 商矩阵, 图, 能量, 下界, 插值, 商矩阵

Abstract: The energy $\mathcal{E}(G)$ of a graph $G$ is the sum of the absolute values of
all the eigenvalues of the adjacency matrix of $G$. It is used in chemistry to
approximate the total $\pi$-electron energy of a molecule. This paper presented some new
lower bounds for $\mathcal{E}(G)$, and characterized those graphs for which these bounds
were attained.

Key words: energy, lower bound, interlace, quotient matrix , graph, energy, lower bound, interlace, quotient matrix

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