Document Type
Article
Publication Date
2013
Publication Title
Electronic Journal of Combinatorics
ISSN
1077-8926
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 σT(w)/σT(u), σT(w)/σT(v), σ(T)/σT(v), and σ(T)/σT(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 FT(w)/FT(u), FT(w)/FT(v), F(T)/FT(v), and F(T)/FT(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 of [Discrete Appl. Math. 80 (1997), 37-56], changing distances to the number of subtrees. We include a number of open problems, shifting the interest towards the number of subtrees in graphs.
Recommended Citation
Székely, László A., Hua Wang.
2013.
"Extremal Values of Ratios: Distance Problems vs. Subtree Problems in Trees."
Electronic Journal of Combinatorics, 20 (1): 1-20.
source: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i1p67
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/216
Comments
The Electronic Journal of Combinatorics is an open access journal in which the author maintains the copyright. Article obtained from The Electronic Journal of Combinatorics.