关于图的距离无符号拉普拉斯谱半径的下界

The lower bound of distance signless Laplacian spectral radius of graphs

若一个连通图G的点集是V(G)={v1,v2,…,vn},那么图G的距离矩阵D(G)=(dij),其中dij表示点vi与vj之间的距离.令TrG(vi)表示点vi到图G中其他所有点的距离之和,Tr(G)表示i行i列位置的元素TrG(vi)的对角矩阵.图G的距离无符号拉普拉斯矩阵QD(G)=Tr(G)+D(G).QD(G)的最大特征值λQ(G)是图G的距离无符号拉普拉斯谱半径.该文确定了给定匹配数的n个点的图的距离无符号拉普拉斯谱半径的下界.

Suppose that the vertex set of a connected graph G is V(G)={v1,v2,…,vn}.Let D(G)=(dij)be the distance matrix of G,where dij is distance between vi and vj.Let TrG(vi)be the sum of distances between vi and all other vertices of G,and Tr(G)be the n×n diagonal matrix with its(i,i)-entry equals to TrG(vi).Then QD(G)=Tr(G)+D(G)is the distance signless Laplacian matrix of G.The largest eigenvalue of QD(G),denoted byλQ(G),is the distance signless Laplacian spectral radius of G.In this paper,the lower bound of distance signless Laplacian spectral radius of n-vertex graphs in terms of matching number is characterized.