#### Title

Greedy Trees and the Extremal Distances

#### Document Type

Presentation

#### Publication Date

6-18-2012

#### Abstract

We show a “universal property’ of the greedy tree with a given degree sequence, namely that the number of pairs of vertices whose distance is at most k is maximized by the greedy tree for all k. This rather strong assertion immediately implies, and is equivalent to, the minimality of the greedy trees with respect to graph invariants of the form Wf (T)= Σ{u,v}⊆V (T ) f(d(u, v)) for any nonnegative, nondecreasing function f. With diﬀerent choices of f, one directly solves the minimization problems of distance-based graph invariants including the classical Wiener index, the Hyper-Wiener index and the generalized Wiener index.

#### Sponsorship/Conference/Institution

Society for Industrial and Applied Mathematics Conference on Discrete Mathematics (SIAM-DM)

#### Location

Halifax, Nova Scotia, Canada

#### Recommended Citation

Wang, Hua.
2012.
"Greedy Trees and the Extremal Distances."
*Mathematical Sciences Faculty Presentations*.
Presentation 517.

https://digitalcommons.georgiasouthern.edu/math-sci-facpres/517