University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 12 3 2021 09 01 Resolvent Energy of Digraphs 139 159 111625 10.22052/ijmc.2021.242877.1562 EN Effat Golpar-Raboky Department of Mathematics, Qom, Iran Azam Babai Department of Mathematics, Qom, Iran Journal Article 2021 06 03 In this paper, we present two approaches to compute the resolvent energy of a digraph . The first method computes the energy by ER(G)=\sum_{i=1})^n\frac{1}{n-Re(z_i)}, where Re(z<sub>_</sub>i )denotes the real part of the eigenvalue z_i of G. In the second method we define ER(G)=\sum_{i=1}^n\frac{1}{n-σ_i}, where σ_i is the ith singular value of G. 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. Resolvent energy singular value Eigenvalue directed graph unicyclic digraph https://ijmc.kashanu.ac.ir/article_111625_6834418b07b921bb7e2d4640c01b3370.pdf