Vol. 5, No. 3, 2012

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Optimal trees for functions of internal distance

Alex Collins, Fedelis Mutiso and Hua Wang

Vol. 5 (2012), No. 3, 371–378
Abstract

The sum of distances between vertices of a tree has been considered from many aspects. The question of characterizing the extremal trees that maximize or minimize various such “distance-based” graph invariants has been extensively studied. Such invariants include, to name a few, the sum of distances between all pairs of vertices and the sum of distances between all pairs of leaves. With respect to the distances between internal vertices, we provide analogous results that characterize the extremal trees that minimize the value of any nonnegative and nondecreasing function of internal distances among trees with various constraints.

Keywords
internal distances, trees, extremal
Mathematical Subject Classification 2010
Primary: 05C05, 05C12
Secondary: 05C30
Milestones
Received: 5 November 2012
Revised: 10 March 2013
Accepted: 30 March 2013
Published: 14 April 2013

Communicated by Jerrold Griggs
Authors
Alex Collins
Department of Mathematics and Statistics
Georgia State University
Atlanta, GA 30303
United States
Fedelis Mutiso
Department of Mathematical Sciences
Georgia Southern University
Statesboro, GA 30460
United States
Hua Wang
Department of Mathematical Sciences
Georgia Southern University
Statesboro, GA 30460
United States