Terminal Wiener TW(G) = Σ d(pᵢ,pⱼ) over pendant (degree-1) vertex pairs only. Gutman-Furtula-Petrović (2009). Ignores internal vertices! Only measures distances between 'endpoints'. Critical for dendrimer characterization and polymer branching analysis.
How to Use
Select graph:
- TW: Terminal Wiener
- Leaves: d=1 only
- vs W: Compare
Dendrimer Applications
Dendrimers: highly branched molecules with many pendant groups. TW measures how spread out the terminal groups are. Low TW: compact, terminals close. High TW: extended, terminals far apart. Critical for drug delivery design.
Bounds
Star: TW = p(p-1) where p = n-1 pendants (all distance 2). Path: TW = (n-1)·1 = n-1 (2 pendants, distance n-1). Balanced trees: TW depends on depth and branching factor.
Step-by-Step Instructions
- 1Select graph.
- 2Identify pendants (d=1).
- 3Compute pairwise distances.
- 4Sum leaf-leaf distances.
- 5Apply to molecules.