最小Q-特征值的扰动定理的推广及其应用（英文）

A Generalization of a Perturbation Theorem on the Least Q-eigenvalue and Its Application

图的最小Q-特征值是图的二部性的一个度量,具有重要的研究意义.本文研究了移接图G的某些二部分支时最小Q-特征值k(G)的变化规律,推广了文献[Linear Algebra Appl.,2012,436(7):2084-2092]中关于κ(G)的扰动定理.作为应用,本文研究了交错定理的等号成立条件,构造了一个非二部连通图类,并对这图类中每个图G构造一个边子集ε,使得对ε的任意子集S都有κ(G)=κ(G-S).

We investigate how the least Q-eigenvalueκ(G)of a graph G changes when some bipartite branches attached at some vertices are relocated to other vertices,and generalize the perturbation theorems onκ(G)given by Wang and Fan in[Linear Algebra Appl.,2012,436(7):2084-2092].As an application,we construct a class of connected non-bipartite graphs and for any graph G in this class we construct a subset E of E(G)such thatκ(G)=κ(G-S)for any subset S ofε.