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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.4 Antofagasta Dec. 2016 

Energy of strongly connected digraphs whose underlying graph is a cycle


Juan Monsalve

Juan Rada 

Universidad de Antioquia



The energy ofa digraph is defined as E (D) =∑1n|Re (zk)|, 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 [3]. When the characteristic polynomial ofa digraph D is ofthe form

where bo (D) = 1 and bk(D) ≥ 0 for all k, we show that

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 ofthe form (0.1). As a consequence, we find the extremal values ofthe energy based on (0.2).

Keywords : digraphs; energy; characteristic polynomial; strongly connected; directed cycles.

AMS Subject Classification: 05C35; 05C50; 05C90.


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Juan Monsalve

Instituto de Matematicas, Universidad de Antioquia Medellln,


e-mail :

Juan Rada

Instituto de Matematicas, Universidad de Antioquia Medellín,


e-mail :

Received : June 2015. Accepted : July 2016

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