Non-cospectral equienergetic trees of diameter at most four

No general method differing from computer search has been discovered for finding noncospectral equienergetic trees. We first utilize techniques of spectral graph theory and Diophantine Equation to analyze the energy of two families of short-diameter trees. Seven infinite families noncospectral equienergetic trees are obtained of which six pairs of them have equal number vertices. This contributes to an open problem posed by Li, Shi and Gutman for constructing noncospectral equienergetic trees.