Improved bounds for the largest eigenvalue of trees

The second largest eigenvalue of trees

Bounds for the Largest Laplacian Eigenvalue of Weighted Graphs

Let G = (V, E) be simple graphs, as graphs which have no loops or parallel edges such that V is a finite set of vertices and E is a set of edges. A weighted graph is a graph each edge of which has been assigned to a square matrix called the weight of the edge. All the weightmatrices are assumed to be of same order and to be positive matrix. In this paper, by “weighted graph” we mean “a weighted...

Bounding the largest eigenvalue of trees in terms of the largest vertex degree∗

On lower bounds for the largest eigenvalue of a symmetric matrix

We consider lower bounds for the largest eigenvalue of a symmetric matrix. In particular we extend a recent approach by Piet Van Mieghem. © 2008 Elsevier Inc. All rights reserved. AMS classification: Primary 15A42; Secondary 30B10

Improved Bounds for the Expected Behaviour of AVL Trees

In this paper we improve previous bounds on expected measures of AVL trees by using fringe analysis. A new way of handling larger tree collections that are not closed is presented. An inherent diiculty posed by the transformations necessary to keep the AVL tree balanced makes its analysis diicult when using fringe analysis methods. We derive a technique to cope with this diiculty obtaining the ...