A sharp upper bound on the spectral radius of generalized weighted digraphs

摘要

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 with the weight that is a non-negative and symmetric matrix of same order of 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].