QUADRATIC FORMS ON GRAPHS WITH APPLICATION TO MINIMIZING THE LEAST EIGENVALUE OF SIGNLESS LAPLACIAN OVER BICYCLIC GRAPHS

被引：0
|
作者：
Yu, Gui-Dong [1 ,2 ]
Fan, Yi-Zheng [1 ]
Wang, Yi [1 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei 230039, Peoples R China
[2] Anqing Normal Coll, Sch Math & Computat Sci, Anqing 246011, Peoples R China
来源：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2014年 / 27卷
基金：
中国国家自然科学基金;
关键词：
Graph; Bicyclic graph; Quadratic form; Least eigenvalue; Signless Laplacian; UNICYCLIC MIXED GRAPH; SPECTRAL-RADIUS; EIGENVECTORS; CONNECTIVITY; NUMBER; BIPARTITENESS; VERTICES; SPREAD; TREES;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a graph and a vector defined on the graph, a quadratic form is defined on the graph depending on its edges. In order to minimize the quadratic form on trees or unicyclic graphs associated with signless Laplacian, the notion of basic edge set of a graph is introduced, and the behavior of the least eigenvalue and the corresponding eigenvectors is investigated. Using these results a characterization of the unique bicyclic graph whose least eigenvalue attains the minimum among all non-bipartite bicyclic graphs of fixed order is obtained.
引用
收藏
页码：213 / 236
页数：24
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