@article{An2024, 
author = {Junfeng An and Yingzhi Tian},
title = {Graphs with a given conditional diameter that maximize the Wiener index},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {15928-15936},
keywords = {Wiener index, diameter, conditional diameter},
url = {https://www.sciopen.com/article/10.3934/math.2024770},
doi = {10.3934/math.2024770},
abstract = {The Wiener index    W  (  G  ) of a graph    G is one of the most well-known topological indices, which is defined as the sum of distances between all pairs of vertices of    G. The diameter    D  (  G  ) of    G is the maximum distance between all pairs of vertices of    G, and the conditional diameter    D  (  G  ;  s  ) is the maximum distance between all pairs of vertex subsets with cardinality    s of    G. When    s  =  1, the conditional diameter    D  (  G  ;  s  ) is just the diameter    D  (  G  ). The authors in [18] characterized the graphs with the maximum Wiener index among all graphs with diameter    D  (  G  )  =  n  −  c, where    1  ≤  c  ≤  4. In this paper, we will characterize the graphs with the maximum Wiener index among all graphs with conditional diameter    D  (  G  ;  s  )  =  n  −  2  s  −  c (   −  1  ≤  c  ≤  1), which extends partial results above.}
}