Decreasing the mean subtree order by adding <i>k</i> edges-Reference-Cited by-同舟云学术

Decreasing the mean subtree order by adding k edges

Published:2023-10-09 Issue:3 Volume:105 Page:357-366
ISSN:0364-9024
Container-title:Journal of Graph Theory
language:en
Short-container-title:Journal of Graph Theory

Author:

Cambie Stijn¹^ORCID,Chen Guantao²,Hao Yanli³,Tokar Nizamettin⁴

Affiliation:

1. Department of Computer Science KU Leuven Campus Kulak Kortrijk Belgium

2. Department of Mathematics and Statistics Georgia State University Altanta Georgia USA

3. School of Mathematics Georgia Institute of Technology Atlanta Georgia USA

4. Department of Mathematics Usak University Usak Turkey

Abstract

AbstractThe mean subtree order of a given graph , denoted , is the average number of vertices in a subtree of . Let be a connected graph. Chin et al. conjectured that if is a proper spanning supergraph of , then . Cameron and Mol disproved this conjecture by showing that there are infinitely many pairs of graphs and with , and such that . They also conjectured that for every positive integer , there exists a pair of graphs and with , , and such that . Furthermore, they proposed that provided . In this note, we confirm these two conjectures.

Publisher

Wiley

Subject

Geometry and Topology,Discrete Mathematics and Combinatorics

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/jgt.23043

Reference11 articles.

1. On the maximum mean subtree order of trees

2. On the mean subtree order of graphs under edge addition

3. Subtrees of graphs

4. Extremal results on average subtree density of series-reduced trees

5. On the average number of nodes in a subtree of a tree

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