Trees with Minimum Weighted Szeged Index Are of a Large Diameter

• Main Authors: Risto Atanasov, Boris Furtula, Riste Škrekovski
• Format: Article
• Language: English
• Published: MDPI AG 2020-05-01
• Series: Symmetry
• Subjects: distance; degree; Szeged index; weighted Szeged index; trees
• Online Access: https://www.mdpi.com/2073-8994/12/5/793

The weighted Szeged index (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>w</mi> <mi>S</mi> <mi>z</mi> </mrow> </semantics> </math> </inline-formula>) has gained considerable attention recently because of its unusual mathematical properties. Searching for a tree (or trees) that minimizes the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>w</mi> <mi>S</mi> <mi>z</mi> </mrow> </semantics> </math> </inline-formula> 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.