Pseudospectrum Energy of Graphs

Document Type : Research Paper


1 Faculty of Computer Science and Mathematics‎, ‎University of Kufa, Najaf‎, ‎Iraq

2 Faculty of Mechanics and Mathematics‎, ‎Belarusian State University‎, ‎Minsk‎, ‎Belarus


Let 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.


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