Issue |
RAIRO-Oper. Res.
Volume 56, Number 1, January-February 2022
|
|
---|---|---|
Page(s) | 415 - 430 | |
DOI | https://doi.org/10.1051/ro/2022010 | |
Published online | 14 February 2022 |
On extremal leaf status and internal status
1
School of Computer Science, South China Normal University, Guangzhou 510631, P.R. China
2
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. China
* Corresponding author: zhoubo@scnu.edu.cn
Received:
19
July
2021
Accepted:
17
January
2022
For a vertex u of a tree T, the leaf (internal, respectively) status of u is the sum of the distances from u to all leaves (internal vertices, respectively) of T. The minimum (maximum, respectively) leaf status of a tree T is the minimum (maximum, respectively) leaf statuses of all vertices of T. The minimum (maximum, respectively) internal status of a tree T is the minimum (maximum, respectively) internal statuses of all vertices of T. We characterize those trees with the smallest (largest, respectively) extremal (minimum and maximum) leaf status and extremal (minimum and maximum) internal status, respectively. We also study the corresponding extremal problems for trees with given parameters, including diameter or maximum degree.
Mathematics Subject Classification: 05C12 / 05C35
Key words: Minimum leaf status / maximum leaf status / minimum internal status / maximum internal status / extremal problem
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.