Extremal iota energy of bicyclic digraphs

摘要

The energy of an n-vertex digraph D is defined by E(D)=∑k=1n|Re(zk)|, where z1,…,zn are eigenvalues of D and Re(zk) is the real part of eigenvalue zk. Very recently, a new type of energy of digraphs has been introduced, which is known as the iota energy of digraphs. The iota energy of the digraph D is defined by Ec(D)=∑k=1n|Im(zk)|, where z1,…,zn are eigenvalues of D and Im(zk) is the imaginary part of eigenvalue zk. The unicyclic digraphs with extremal iota energy are known. In this paper, we consider a class Dn of n-vertex bicyclic digraphs with vertex-disjoint directed cycles and find the digraphs in Dn with minimal and maximal iota energy.