An alternative proof of the Sombor index minimizing property of greedy trees

Recently, Gutman defined a new graph invariant which is named the Sombor index SO(G) of G and computed via expression = ?u~v? qdeg(u)2 + deg(v)2, where deg(u) represents degree vertex u in summing performed across all unordered pairs adjacent vertices v. Damnjanovic et al. have implemented an earlier result obtained by Wang order to show that, among trees TD that specified sequence D, greedy tree must attain minimum index. Here we provide alternative proof this same constructing auxiliary pseudo-Sombor without relying on any other results.