A Sharp Upper Bound on the Spectral Radius of Generalized Weighted Digraphs

Abstract

A generalized weighted digraph \(G = (V, E)\) is a digraph with \(n\) vertices and \(m\) arcs without loops and multiarcs, where each arc is assigned a weight that is a non-negative and symmetric matrix of order \(p\). In this paper, we give a sharp upper bound for the spectral radius of generalized weighted digraphs (see Theorem 2.7), which generalizes some other results on the spectral radius of weighted digraphs in [4], [11], and [16].