BLOOMFIELD-WATSON-KNOTT TYPE INEQUALITIES FOR EIGENVALUES

Payne-polya-weinberger Type Inequalities for Eigenvalues of Nonelliptic Operators

Let denote the Laplacian in the Euclidean space. The classic upper estimates, independent of the domain, for the gaps of eigenvalues of − , (− )2 and (− )k(k ≥ 3) were studied extensively by many mathematicians, cf. Payne, Polya and Weinberger [16], Hile and Yeh [10], Chen and Qian [2], Guo [8] etc.. The asymptotic behaviors of eigenvalues for degenerate elliptic operators were considered by Be...

Nordhaus-Gaddum Type Inequalities for Laplacian and Signless Laplacian Eigenvalues

Let G be a graph with n vertices. We denote the largest signless Laplacian eigenvalue of G by q1(G) and Laplacian eigenvalues of G by μ1(G) > · · · > μn−1(G) > μn(G) = 0. It is a conjecture on Laplacian spread of graphs that μ1(G)−μn−1(G) 6 n − 1 or equivalently μ1(G) + μ1(G) 6 2n − 1. We prove the conjecture for bipartite graphs. Also we show that for any bipartite graph G, μ1(G)μ1(G) 6 n(n − ...

On Bernstein Type Inequalities for Complex Polynomial

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

Isoperimetric Inequalities and Eigenvalues

Isoperimetric Inequalities and Eigenvalues

An upper bound is given on the minimum distance between i subsets of the same size of a regular graph in terms of the i-th largest eigenvalue in absolute value. This yields a bound on the diameter in terms of the i-th largest eigenvalue, for any integer i. Our bounds are shown to be asymptotically tight. A recent result by Quenell relating the diameter, the second eigenvalue, and the girth of a...