On Principal Eigenvalues ofp-Laplacian-like Operators

The Spectral Function and Principal Eigenvalues for Schrdinger Operators

Let m 2 Lloc(R N ); 0 6= m+ in Kato’s class. We investigate the spectral function 7! s( + m)where s( + m) denotes the upper bound of the spectrum of the Schrödinger operator + m. In particular, we determine its derivative at 0. If m is sufficiently large, we show that there exists a unique 1 > 0 such that s( + 1m) = 0. Under suitable conditions on m it follows that 0 is an eigenvalue of + 1m wi...

Some remarks on Laplacian eigenvalues and Laplacian energy of graphs

Suppose μ1, μ2, ... , μn are Laplacian eigenvalues of a graph G. The Laplacian energy of G is defined as LE(G) = ∑n i=1 |μi − 2m/n|. In this paper, some new bounds for the Laplacian eigenvalues and Laplacian energy of some special types of the subgraphs of Kn are presented. AMS subject classifications: 05C50

Bounds on normalized Laplacian eigenvalues of graphs

*Correspondence: [email protected] 1School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian, P.R. China 2Center for Discrete Mathematics, Fuzhou University, Fuzhou, Fujian, P.R. China Full list of author information is available at the end of the article Abstract Let G be a simple connected graph of order n, where n≥ 2. Its normalized Laplacian eigenvalues are 0 = λ1 ...

On Laplacian Eigenvalues of a Graph

Let G be a connected graph with n vertices and m edges. The Laplacian eigenvalues are denoted by μ1(G) ≥ μ2(G) ≥ ·· · ≥ μn−1(G) > μn(G) = 0. The Laplacian eigenvalues have important applications in theoretical chemistry. We present upper bounds for μ1(G)+ · · ·+μk(G) and lower bounds for μn−1(G)+ · · ·+μn−k(G) in terms of n and m, where 1 ≤ k ≤ n−2, and characterize the extremal cases. We also ...

Bibliography on the Signless Laplacian Eigenvalues