Optimal Trees for Functions of Internal Distance

Document Type

Article

Publication Date

2012

Publication Title

Involve

DOI

10.2140/involve.2012.5.371

ISSN

1944-4184

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.

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