University of KashanIranian Journal of Mathematical Chemistry2228-648911220200701Pseudospectrum Energy of Graphs839310984610.22052/ijmc.2020.221182.1488ENHahderShelashFaculty of Computer Science and Mathematics, University of Kufa, Najaf, IraqAliShukurFaculty of Mechanics and Mathematics, Belarusian State University, Minsk, Belarus0000-0003-3513-9216Journal Article20200224Let G be a simple graph of order N, the concept of resol-vent energy of graph G; i.e. ER(G)=\sum_{i=1}^N (N - λi)^{-1} was established in Resolvent Energy of Graphs, MATCH commun. Math. comput. chem., 75 (2016), 279-290. In this paper we study the set of resol-vents energies of graph G which it is called pseudospectrum energy of graph PS(G). For large value resolvent energy of graph ER(G) and real eigenvalues, we establish a number of properties of PS(G): For complex eigenvalues, some examples of PS(G) are given.https://ijmc.kashanu.ac.ir/article_109846_ffd2d02d93001914f9a1577b7f1fe61b.pdf