IMPROVED BOUNDS FOR THE SPECTRAL RADIUS OF DIGRAPHS

Abstract

Let G = (V, E) be a digraph with n vertices and m arcs without loops and multi-arcs. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. In this note, we obtain two sharp upper and lower bounds on ρ(G). These bounds improve those obtained by G. H. Xu and C.-Q Xu (Sharp bounds for the spectral radius of digraphs, Linear Algebra Appl. 430, 1607–1612, 2009).