The maximum spectral radius of irregular bipartite graphs

The Spectral Radius and the Maximum Degree of Irregular Graphs

Let G be an irregular graph on n vertices with maximum degree ∆ and diameter D. We show that ∆ − λ1 > 1 nD , where λ1 is the largest eigenvalue of the adjacency matrix of G. We also study the effect of adding or removing few edges on the spectral radius of a regular graph. 1 Preliminaries Our graph notation is standard (see West [22]). For a graph G, we denote by λi(G) the i-th largest eigenval...

Spectral radius of bipartite graphs

On the distance spectral radius of bipartite graphs

Article history: Received 11 June 2011 Accepted 29 July 2011 Available online 27 August 2011 Submitted by R.A. Brualdi AMS classification: 05C50 15A18

On the spectral radius of bipartite graphs with given diameter

Article history: Received 17 March 2008 Accepted 9 October 2008 Available online 3 December 2008 Submitted by R.A. Brualdi AMS classification: 05C50

Spectral radius and maximum degree of connected graphs

Given a connected irregular graph G of order n, write μ for the largest eigenvalue of its adjacency matrix, ∆ for its maximum degree, andD for its diameter. We prove that ∆− μ > 1 (D + 2)n and this bound is tight up to a constant factor. This improves previous results of Stevanović and Zhang, and extends a result of Alon and Sudakov.