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 b...
- 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/
| Summary: | 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). |
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