Energy of strongly connected digraphs whose underlying graph is a cycle

The energy of a digraph is defined as E (D) =∑1n|Re (z k)|, where z1,..., z n 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 ofa digraph D is ofthe form <img width=38...

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Autores principales:	Monsalve,Juan, Rada,Juan
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2016
Materias:	digraphs energy characteristic polynomial strongly connected directed cycles
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400003
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spelling	oai:scielo:S0716-091720160004000032017-01-05Energy of strongly connected digraphs whose underlying graph is a cycleMonsalve,JuanRada,Juan digraphs energy characteristic polynomial strongly connected directed cycles The energy of a digraph is defined as E (D) =∑1n\|Re (z k)\|, where z1,..., z n 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 ofa digraph D is ofthe form <img width=387 height=66 src="../../../../../Users/Raul%20Jimenez/Desktop/F01art01.jpg"> where bo (D) = 1 and b k(D) ≥ 0 for all k, we show that <img src="../imagenes/F02art01.jpg" alt="" width="385" height="72"> 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).info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.35 n.4 20162016-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400003en10.4067/S0716-09172016000400003
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	digraphs energy characteristic polynomial strongly connected directed cycles
spellingShingle	digraphs energy characteristic polynomial strongly connected directed cycles Monsalve,Juan Rada,Juan Energy of strongly connected digraphs whose underlying graph is a cycle
description	The energy of a digraph is defined as E (D) =∑1n\|Re (z k)\|, where z1,..., z n 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 ofa digraph D is ofthe form <img width=387 height=66 src="../../../../../Users/Raul%20Jimenez/Desktop/F01art01.jpg"> where bo (D) = 1 and b k(D) ≥ 0 for all k, we show that <img src="../imagenes/F02art01.jpg" alt="" width="385" height="72"> 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).
author	Monsalve,Juan Rada,Juan
author_facet	Monsalve,Juan Rada,Juan
author_sort	Monsalve,Juan
title	Energy of strongly connected digraphs whose underlying graph is a cycle
title_short	Energy of strongly connected digraphs whose underlying graph is a cycle
title_full	Energy of strongly connected digraphs whose underlying graph is a cycle
title_fullStr	Energy of strongly connected digraphs whose underlying graph is a cycle
title_full_unstemmed	Energy of strongly connected digraphs whose underlying graph is a cycle
title_sort	energy of strongly connected digraphs whose underlying graph is a cycle
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2016
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400003
work_keys_str_mv	AT monsalvejuan energyofstronglyconnecteddigraphswhoseunderlyinggraphisacycle AT radajuan energyofstronglyconnecteddigraphswhoseunderlyinggraphisacycle
_version_	1718439817144958976

Energy of strongly connected digraphs whose underlying graph is a cycle

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