华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (3): 1-5.

• 应用数学与基础数学 •    下一篇

图的最小Q-特征值

何常香, 周 敏   

  1. 上海理工大学~~理学院, 上海 200093
  • 收稿日期:2011-05-01 修回日期:2011-08-01 出版日期:2012-05-25 发布日期:2012-05-22

Least Q-eigenvalue of a graph

HE Chang-xiang, ZHOU Min   

  1. College of Science,  University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2011-05-01 Revised:2011-08-01 Online:2012-05-25 Published:2012-05-22

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摘要： 证明了, 若连通图\,$G$\,不是二部图, 则其最小\,$Q$\,-特征值\,$q(G)\geqslant \frac{1}{n(D+1)}$, 其中\,$D$\,是\,$G$\,的直径. 另外, 还给出了图\,$G$\,的最小\,$Q$-特征值与其子图的最小\,$Q$\,-特征值之间的关系.

关键词: 非二部图, $Q$-特征值, 直径

Abstract: We showed that: If $G$ is a non-bipartite connected graph, then $q(G)\geqslant \frac{1}{n(D+1)}$, where $g(G)$ is the least $Q$-eigenvalue of $G$, and $D$ is the diameter of $G$. Some relations between the least $Q$-eigenvalue of $G$ and that of its subgraph were given.

Key words: non-bipartite graph, $Q$-eigenvalue, diameter

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