On the p-reduced Energy of a Graph

Mirjana Lazić

Let G be a simple connected graph of order n and let $\lambda_1 \geq \lambda_2 \geq \dots \geq \lambda_n$ be the spectrum of G. Then the sum $S^{l}_{k}(G)= \abs{\lambda_{k+1}}+\abs{\lambda_{k+2}}+ \cdots + \abs{\lambda_{n-l}}$ is called (k, l)-reduced energy of G, where k, l are two fixed nonnegative integers [2]. In this work, we make a generalization of the (k, l)-reduced energy, as follows: for any fixed $p \in N$, the sum $S^{l}_{k}(G, p)= \abs{\lambda_{k+1}}^p+\abs{\lambda_{k+2}}^p+ \cdots + \abs{\lambda_{n-l}}^p$ is called the p-th (k, l)-reduced energy of the graph G. We also here introduce definitions of some other kinds of the p-reduced energies and we prove some properties of them.