On the energy of digraphs

2019/09/16 by Juan R. Carmona, Carmona, Juan R.
Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1909.07312

openalex publication_date 2019/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let D be a simple digraph with eigenvalues z₁,z₂,...,z_n. The energy of D is defined as E(D)= ∑_i=1ⁿ |Re(z_i)|, is the real part of the eigenvalue z_i. In this paper a lower bound will be obtained for the spectral radius of D, wich improves some the lower bounds that appear in the literature \citeG-R, \citeT-C. This result allows us to obtain an upper bound for the energy of D . Finally, digraphs are characterized in which this upper bound improves the bounds given in \citeG-R and \citeT-C.

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