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Hermitian energy and Hermitian Estrada index of digraphs. (English) Zbl 1458.05143

Summary: Let \(X\) be a digraph of order \(n\), and \(\alpha_1, \alpha_2,\ldots, \alpha_n\) 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.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C20 Directed graphs (digraphs), tournaments
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