#### Title

Distance-Based Functions of Trees

#### Document Type

Presentation

#### Publication Date

3-10-2012

#### 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) = P{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

Spring Southeastern Sectional Meeting of the American Mathematical Society (AMS)

#### Location

Tampa, FL

#### Recommended Citation

Wang, Hua.
2012.
"Distance-Based Functions of Trees."
*Mathematical Sciences Faculty Presentations*.
Presentation 509.

https://digitalcommons.georgiasouthern.edu/math-sci-facpres/509