Some new bounds on resolvent energy of a graph

Source abstract

Abstract Let G G be a simple graph of order n n with eigenvalues λ 1 ≥ λ 2 ≥ … ≥ λ n . {\lambda }_{1}\ge {\lambda }_{2}\ge \ldots \ge {\lambda }_{n}. The resolvent energy of G G is a spectrum-based graph invariant defined as ER ( G ) = ∑ i = 1 n ( n − λ i ) − 1 . {\rm{ER}}(G)={\sum }_{i=1}^{n}{(n-{\lambda }_{i})}^{-1}. In this work, we propose some new bounds for ER ( G ) {\rm{ER}}(G) . As a direct consequence of these bounds, we present some ( n , m ) (n,m) -type results for triangle-free graphs.