Trees with Minimum Weighted Szeged Index Are of a Large Diameter

Abstract

The weighted Szeged index ( w S z ) has gained considerable attention recently because of its unusual mathematical properties. Searching for a tree (or trees) that minimizes the w S z 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.

Keywords

• distance
• degree
• Szeged index
• weighted Szeged index
• trees