Open problems for equienergetic graphs

Abstract

The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Two graphs of the same order are said to be equienergetic if their energies are equal. We point out the following two open problems for equienergetic graphs. (1) Although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pair. (2) If by numerical calculation one finds that two non-cospectral graphs seem to be equienergetic, in the general case no method is known for proving that this indeed is the case.