论文信息 - Upper Bounds for the Laplacian Graph Eigenvalues

Upper Bounds for the Laplacian Graph Eigenvalues

We first apply non-negative matrix theory to the matrix K=D+A, where D and A are the degree-diagonal and adjacency matrices of a graph G, respectively, to establish a relation on the largest Laplacian eigenvalue λ1(G) of G and the spectral radius ρ(K) of K. And then by using this relation we present two upper bounds for λ1(G) and determine the extrernal graphs which achieve the upper bounds.

Jiong Sheng Li | Yong Liang Pan

[1] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2] V. Sunder,et al. The Laplacian spectrum of a graph , 1990 .

[3] Bo Zhou,et al. On Laplacian Eigenvalues of a Graph , 2004 .

[4] R. Merris. Laplacian matrices of graphs: a survey , 1994 .

[5] B. Mohar. THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[6] B. Mohar. Some applications of Laplace eigenvalues of graphs , 1997 .

[7] T. D. Morley,et al. Eigenvalues of the Laplacian of a graph , 1985 .

[8] Zhang Xiaodong,et al. A new upper bound for eigenvalues of the laplacian matrix of a graph , 1997 .

[9] Yong-Liang Pan,et al. A note on the second largest eigenvalue of the laplacian matrix of a graph , 2000 .

[10] Russell Merris,et al. The Laplacian Spectrum of a Graph II , 1994, SIAM J. Discret. Math..

[11] Michael William Newman,et al. The Laplacian spectrum of graphs , 2001 .

[12] R. Merris. A note on Laplacian graph eigenvalues , 1998 .