Energy of strongly connected digraphs whose underlying graph is a cycle (2016)
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).