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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (4): 468-478.doi: 10.3969/j.issn.1005-3085.2018.04.009

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第二小距离特征值在给定区间中所确定的图（英）

翟丹丹   

  1. 华东理工大学数学系，上海  200237
  • 收稿日期:2015-09-08 接受日期:2017-06-20 出版日期:2018-08-15 发布日期:2018-10-15

Graphs Determined by Second Smallest Distance Eigenvalues in Given Intervals

ZHAI Dan-dan   

  1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237
  • Received:2015-09-08 Accepted:2017-06-20 Online:2018-08-15 Published:2018-10-15

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摘要： 令$G=(V,E)$是一个具有$n$个顶点的简单无向图．对于任意一个$n$阶简单无向图，它有$n$个距离特征值．本文主要研究其中第二小距离特征值．利用了禁用子图的方法，刻画了在区间$\lambda_{n-1}(D(G))\in [-2.4295,0]$中的所有树，以及满足$\lambda_{n-1}(D(G))\in [-2,0]$的所有单圈图和双圈图．

关键词: 第二小距离特征值, 树, 单圈图, 双圈图

Abstract: Let $G=(V,E)$ be a simplified connected graph with $n$ vertices. For a simplified connected graph with $n$ vertices, it has $n$ distance eigenvalues. The second small distance eigenvalue is studied mainly in this paper. And method of disabling the subgraph is used to characterize trees with $\lambda_{n-1}(D(G))\in [-2.4295,0]$, unicyclic and bicyclic graphs with $\lambda_{n-1}(D(G))\in [-2,0]$.

Key words: the second smallest distance eigenvalue, trees, unicyclic graphs, bicyclic graphs

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