The spectral radius and the maximum degree of irregular graphs
Abstract
Description
Let $G$ be an irregular graph on $n$ vertices with maximum degree $Δ$ and diameter $D$. We show that Δ-λ_1>\frac{1}{nD} where $λ_1$ 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.
10 pages, 1 figure, submitted to EJC on January 20, 2007
10 pages, 1 figure, submitted to EJC on January 20, 2007