Energy and NEPS of graphs

Abstract

The energy of a graph is the sum of the absolute values of the eigenvalues of the graph. We study the energy of the noncomplete extended p-sum (NEPS) of the graphs, a very general composition of the graphs in which the special case is the product of graphs. We show that the energy of the product of graphs is the product of the energy of graphs, and how this result may be used to construct arbitrarily large families of noncospectral connected graphs having the same number of vertices and the same energy. Further, unlike the product, we show that the energy of any other NEPS of the graphs cannot be represented as a function of the energy of starting graphs.