Hermitian energy and Hermitian Estrada index of digraphs

Abstract

Let [Formula: see text] be a digraph of order [Formula: see text], and [Formula: see text] be spectrum of the Hermitian adjacency matrix. The main purpose of this paper is to introduce the Hermitian energy and Hermitian Estrada index of a digraph, both based on the eigenvalues of the Hermitian matrix. Moreover, we establish upper and lower bounds for these new digraph invariants, and relations between them.