@article{Su2024, 
author = {Zhenhua Su and Zikai Tang},
title = {Minimum distance–unbalancedness of the merged graph of        C    3   and a tree},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {16863-16875},
keywords = {distance–unbalancedness, distance–balanced graph, Mostar index},
url = {https://www.sciopen.com/article/10.3934/math.2024818},
doi = {10.3934/math.2024818},
abstract = {For a graph    G, let        n    G    (  u  ,  v  ) be the number of vertices of    G that are strictly closer to    u than to    v. The distance–unbalancedness index        u    B    (  G  ) is defined as the sum of        |        n    G    (  u  ,  v  )  −      n    G    (  v  ,  u  )      |   over all unordered pairs of vertices    u and    v of    G. In this paper, we show that the minimum distance–unbalancedness of the merged graph        C    3    ⋅  T is    (  n  +  2  )  (  n  −  3  ), where        C    3    ⋅  T is obtained by attaching a tree    T to the cycle        C    3  .}
}