Trees with minimum weighted szeged index are of a large diameter

Abstract

© 2020 by the authors. The weighted Szeged index (wSz) has gained considerable attention recently because of its unusual mathematical properties. Searching for a tree (or trees) that minimizes the wSz is still going on. Several structural details of a minimal tree were described. Here, it is shown a surprising property that these trees have maximum degree at most 16, and as a consequence, we promptly conclude that these trees are of large diameter.