Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova
Abstract
Let G be a finite simple undirected graph with n vertices and m edges. The Harmonic energy of a graph G, denoted by HE(G), is defined as the sum of the absolute
values of all Harmonic eigenvalues of G. The Harmonic Estrada index of a graph G, denoted by HEE(G), is defined as HEE=HEE(G)=∑i=1neγi,
where γ1⩾γ2⩾⋯⩾γn are the H-eigenvalues of G.
In this paper we present some new bounds for HE(G) and HEE(G) in terms of number of vertices, number of edges and the sum-connectivity index