Some kinds of energies of graphs (Q1322190)

Let \(\lambda_ 1 \geq \lambda_ 2 \geq \cdots \geq \lambda_ n\) be the spectrum of a graph \(G\) of order \(n\), and let \(k\), \(l \geq 0\) be any nonnegative integers such that \(k + l<n\). The sum \(\sum^{n- l}_{\nu=k+1} | \lambda_ \nu |\) is called the reduced \((k, l) \)-energy of \(G\). For an arbitrary real constant \(\alpha \geq 1\), three theorems on finiteness of the set of all graphs whose reduced \((k,l)\)- energy does not exceed \(\alpha\), are proved.