Energy of strongly connected digraphs whose underlying graph is a cycle

The energy of a digraph is defined as E (D) = Pnk= where z1,...,zn are the eigenvalues of the adjacency matrix of D. This is a generalization of the concept of energy introduced by I. Gutman in 1978. When the characteristic polynomial of a digraph D is of the form (0.1) φD (z) = where b0 (D)=1 and bk (D) ≥ 0 for all k, we show that (0.2) E (D) = 2π… This expression for the energy has many applications in the study of extremal values of the energy in special classes of digraphs. In this paper we consider the set D∗ (Cn) of all strongly connected digraphs whose underlying graph is the cycle Cn, and characterize those whose characteristic polynomial is of the form (0.1). As a consequence, we find the extremal values of the energy based on (0.2).

• Autores: Monsalve Aristazábal, Juan Daniel; Rada Rincón, Juan Pablo
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2016
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/45971
• Acceso en línea: https://hdl.handle.net/10495/45971
• Palabra clave: Directed graphs; Energía; Energy; Polinomios; Polynomials; http://id.loc.gov/authorities/subjects/sh85038262; http://id.loc.gov/authorities/subjects/sh2002010497; http://id.loc.gov/authorities/subjects/sh85104702
• Rights: openAccess
• License: http://creativecommons.org/licenses/by/4.0/