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Proyecciones (Antofagasta)

Print version ISSN 0716-0917


MONSALVE, Juan  and  RADA, Juan. Energy of strongly connected digraphs whose underlying graph is a cycle. Proyecciones (Antofagasta) [online]. 2016, vol.35, n.4, pp.395-404. ISSN 0716-0917.

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

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

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