## Abstract

The authors discovered a dual behaviour of two tree indices, the Wiener index and the number of subtrees, for a number of extremal problems [Discrete Appl. Math. 155 (3) 2006, 374-385; Adv. Appl. Math. 34 (2005), 138-155]. Barefoot, Entringer and Székely [Discrete Appl. Math. 80(1997), 37-56] determined extremal values of σ_{T}(w)/σ_{T}(u), σ_{T} (w)/σ_{T} (v), σ(T)/σ_{T}(v), and σ(T)/σ_{T} (w), where T is a tree on n vertices, v is in the centroid of the tree T, and u,w are leaves in T. In this paper we test how far the negative correlation between distances and subtrees go if we look for the extremal values of F_{T} (w)/F_{T} (u), F_{T} (w)/F_{T} (v), F(T)/F_{T} (v), and F(T)/F_{T} (w), where T is a tree on n vertices, v is in the subtree core of the tree T, and u, w are leaves in T-the complete analogue, changing distances to the number of subtrees. We include a number of open problems, shifting the interest towards the number of subtrees in graphs.

Original language | American English |
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Journal | Electronic Journal of Combinatorics |

Volume | 20 |

State | Published - Jan 1 2013 |

## Keywords

- Binary tree
- Caterpillar
- Center
- Centroid
- Distances in trees
- Extremal problems
- Good binary tree
- Star tree
- Subtree core
- Subtrees of trees
- Tree
- Wiener index

## DC Disciplines

- Education
- Mathematics