Distance-Based Functions of Trees

Research output: Contribution to conferencePresentation

Abstract

<div class="line" id="line-5"> We show a &ldquo;universal property&rdquo; 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}&sube;V (T) f(d(u, v)) for any nonnegative, nondecreasing function f. With di&fflig;erent 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.</div>
Original languageAmerican English
StatePublished - Mar 10 2012
EventSpring Southeastern Sectional Meeting of the American Mathematical Society (AMS) -
Duration: Mar 6 2016 → …

Conference

ConferenceSpring Southeastern Sectional Meeting of the American Mathematical Society (AMS)
Period03/6/16 → …

Disciplines

  • Mathematics

Keywords

  • Distance-based functions
  • Trees

Fingerprint

Dive into the research topics of 'Distance-Based Functions of Trees'. Together they form a unique fingerprint.

Cite this