一类树的主特征值数目刻画  

Characterization of the Number of Main Eigenvalues of a Class of Trees

作　　者：杜泽楠 于倩 

机构地区：[1]长安大学,理学院,陕西 西安

出　　处：《运筹与模糊学》2021年第2期131-136,共6页Operations Research and Fuzziology

摘　　要：一个图的邻接矩阵的特征值称为图的特征值,图的所有特征值的多重集称为图的谱。如果图的一个特征值所对应的特征空间与全1向量不正交,则称其为主特征值,主特征值对于刻画图及研究图的性质都有重要的意义。刻画恰有k(2≤k≤n)个主特征值的图是一个存在已久的问题,本文给出了一类树的主特征值数目的下界。The eigenvalues of the adjacency matrix of a graph are called the eigenvalues of a graph, the multi-set of all eigenvalues of a graph is called the spectrum of a graph. An eigenvalue of a graph is a main eigenvalue if its eigenspace is not orthogonal to the all-ones vector, the main eigenvalues are significant to the characterization of graphs and the properties of graphs. Characterizing graphs with k(2≤k≤n) number of main eigenvalues are a long-standing problem. In this paper, the lower bound of main eigenvalues of a class of trees is determined.

关 键 词：邻接矩阵 主特征值 树图 

分 类 号：O15[理学—数学]