Relationship between Ordinary, Laplacian, Randić, Incidence, and Sombor Energies of Trees

Abstract

The sum of the absolute values of the eigenvalues of the graph’s adjacency matrix is known as its ordinary energy. Based on the eigenvalues of a range of other graph matrices, several other equivalent energies are being considered. In this work, we considered ordinary energy, Laplacian, Randi´c, incidence, and Sombor energy to analyze their relationship using polynomial regression. The performance of each model is exceptional with cross-validation RMSE mostly below 1.