Different central parts of trees and their pairwise distances

ABSTRACT

We determine the tree which maximizes the distance between characteristic set and subtree core over all trees on n vertices. The asymptotic nature of this distance is also discussed. The problem of extremizing the distance between different central parts of trees on n vertices with fixed diameter is studied.

Keywords:

• Centre
• centroid
• characteristic set
• subtree core
• tree

AMS Subject Classifications:

• 05C05
• 05C12
• 05C50

Acknowledgements

The authors wish to sincerely thank the referee for his/her detailed comments and suggestions, thus improving the submitted version of the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported by University Grants Commission (UGC) Fellowship scheme (Sr. No. 2061641145), Government of India.