Proof of a Conjecture on Sombor Index and the Least Sombor Eigenvalue of Graphs

Let G be a simple graph with vertex set V (G) = {v1, v2, . . ., vn} and edge set E(G), where |V (G)| = n and |E(G)| = m.Molecular descriptors play a significant role in quantitative studies of structureproperty and structure-activity relationships.One of the popular degree-based topological indices, the Sombor index (SO), is a chemically useful descriptor.The Sombor index of a graph G is defined as