A Note on the Signless Laplacian and Distance Signless Laplacian Eigenvalues of Graphs  

作　　者：Fenglei TIAN Xiaoming LI Jianling ROU 

机构地区：[1]Department of Mathematics, China University of Mining and Technology

出　　处：《Journal of Mathematical Research with Applications》2014年第6期647-654,共8页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11171343)

摘　　要：Let G be a simple graph. We first show that δ≥di-√[i/2][i/2], where δiand di denote the i-th signless Laplacian eigenvalue and the i-th degree of vertex in G, respectively.Suppose G is a simple and connected graph, then some inequalities on the distance signless Laplacian eigenvalues are obtained by deleting some vertices and some edges from G. In addition, for the distance signless Laplacian spectral radius ρQ（G）, we determine the extremal graphs with the minimum ρQ（G） among the trees with given diameter, the unicyclic and bicyclic graphs with given girth, respectively.Let G be a simple graph. We first show that δ≥di-√[i/2][i/2], where δiand di denote the i-th signless Laplacian eigenvalue and the i-th degree of vertex in G, respectively.Suppose G is a simple and connected graph, then some inequalities on the distance signless Laplacian eigenvalues are obtained by deleting some vertices and some edges from G. In addition, for the distance signless Laplacian spectral radius ρQ（G）, we determine the extremal graphs with the minimum ρQ（G） among the trees with given diameter, the unicyclic and bicyclic graphs with given girth, respectively.

关 键 词：signless Laplacian distance signless Laplacian spectral radius eigenvalues 

分 类 号：O157.5[理学—数学] O177.91[理学—基础数学]