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

Abstract

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