Molecular trees with extremal values of Sombor indices

Based on elementary geometry, a class of novel graph invariants was introduced by Gutman, of which the simplest is the Sombor index SO, defineddenotes the degree of v in G. In this paper, the chemical importance of the Sombor index is investigated and it is shown that the new index is useful in predicting physico-chemical properties with high accuracy compared to some well-established and often used indices. We obtain a sharp upper bound for the Sombor index among all molecular trees with fixed numbers of vertices, and characterize those molecular trees achieving the extremal value. Also, we obtain the extremal values of the reduced Sombor index for molecular trees.