pseudospectrum energy of graphs

Let g be a simple graph of order n, the concept of resolvent 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), 279290. in this paper we study the set of resolvents 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.