Construction of Equienergetic Trees

The energy E(G) of a graph G is the sum of the absolute values of all eigenvalues of G. Two graphs of the same order are said to be equienergetic if their energies are equal. As pointed out by Gutman, it is not known how to systematically construct any pair of equienergetic, non-cospectral trees until now. Inspired by the research of integral trees, we proposed a construction of infinite pairs of equienergetic trees of diameter 4.