The lower bound of distance signless Laplacian spectral radius of graphs
ZHU Yinfen1， WANG Guoping2， CHEN Xing1
1.Xinjiang Institute of Engineering Institute of Mathematical， Urumqi 830029，China；2.Department of Mathematics， Xinjiang Normal University， Urumqi 830017，China
Abstract：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 by λQ(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.
2021, Vol. 55 
