On the ordering of bicyclic digraphs with respect to energy and iota energy

Let z₁,z₂,…,z_n be eigenvalues of the adjacency matrix of an n-vertex digraph D. Let Re(z_k) and Im(z_k) denote the real part and the imaginary part of eigenvalue z_k, respectively. The energy of an n-vertex digraph D is defined as E(D)=∑_k=1 ⁿ|Re(z_k)|. Recently, the concept of energy of digraphs is extended to iota energy of digraphs. The iota energy of an n-vertex digraph D is defined as E_c(D)=∑_k=1 ⁿ|Im(z_k)|. In this paper, we investigate the energy and iota energy about a class D_n of n-vertex bicyclic digraphs with vertex-disjoint two directed even cycles and characterize the digraphs in D_n with maximal and minimal energy or iota energy. Moreover, we determine the whole ordering in D_n with respect to energy and iota energy, respectively.