论文标题
树木的最小距离不平衡
Minimum distance-unbalancedness of trees
论文作者
论文摘要
对于图$ g $，以及两个不同的顶点$ u $和$ g $的$ v $，让$ n_g（u，v）$是$ g $的顶点的数量，$ g $ in $ g $更接近$ u $，而不是$ v $。 Miklavič和šparl（Arxiv：2011.01635v1）将$ g $的距离不平衡度定义为$ | n_g（u，v）-n_g（v，u）| $的总和。我们证实了他们的一种猜想，我们表明恒星最大程度地减少了固定秩序的所有树木之间的距离不平衡。
For a graph $G$, and two distinct vertices $u$ and $v$ of $G$, let $n_G(u,v)$ be the number of vertices of $G$ that are closer in $G$ to $u$ than to $v$. Miklavič and Šparl (arXiv:2011.01635v1) define the distance-unbalancedness of $G$ as the sum of $|n_G(u,v)-n_G(v,u)|$ over all unordered pairs of distinct vertices $u$ and $v$ of $G$. Confirming one of their conjectures, we show that the stars minimize the distance-unbalancedness among all trees of a fixed order.
