Let G be a simple connected graph with order n.Let L(G)and Q(G)be the normalized Laplacian and normalized signless Laplacian matrices of G,respectively.Letλk(G)be the k-th smallest normalized Laplacian eigenvalue of ...Let G be a simple connected graph with order n.Let L(G)and Q(G)be the normalized Laplacian and normalized signless Laplacian matrices of G,respectively.Letλk(G)be the k-th smallest normalized Laplacian eigenvalue of G.Denote byρ(A)the spectral radius of the matrix A.In this paper,we study the behaviors ofλ2(G)andρ(L(G))when the graph is perturbed by three operations.We also study the properties ofρ(L(G))and X for the connected bipartite graphs,where X is a unit eigenvector of L(G)corresponding toρ(L(G)).Meanwhile we characterize all the simple connected graphs withρ(L(G))=ρ(Q(G)).展开更多
基金by the National Natural Science Foundation of China(No.11871398)the Natural Science Basic Research Plan in Shaanxi Province of China(Program No.2018JM1032)the Fundamental Research Funds for the Central Universities(No.3102019ghjd003).
文摘Let G be a simple connected graph with order n.Let L(G)and Q(G)be the normalized Laplacian and normalized signless Laplacian matrices of G,respectively.Letλk(G)be the k-th smallest normalized Laplacian eigenvalue of G.Denote byρ(A)the spectral radius of the matrix A.In this paper,we study the behaviors ofλ2(G)andρ(L(G))when the graph is perturbed by three operations.We also study the properties ofρ(L(G))and X for the connected bipartite graphs,where X is a unit eigenvector of L(G)corresponding toρ(L(G)).Meanwhile we characterize all the simple connected graphs withρ(L(G))=ρ(Q(G)).
