Resolvent Energy of Digraphs

چکیده مقاله

The resolvent energy of a graph G is defined as ER(G) = (Formula presented), where (Formula presented) the eigenvalues of the adjacency matrix of G. We extend this concept to directed graphs with two approaches. The first approach, consider (Formula presented) where (Formula presented) are the singular values of G. The second approach, define the resolvent energy of a digraph G by (Formula presented) where z₁…, z_n are the eigenvalues of G and Re(z_i) denotes the real part of Z_i. We prove some properties of resolvent energy for some special digraphs and determine the resolvent energy of unicyclic and bicyclic digraphs and present lower bound for resolvent energy of directed cycles. © 2021. University of Kashan Press. All rights reserved