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Extremal total distance of graphs of given radius I
Journal of Graph Theory ( IF 0.9 ) Pub Date : 2020-11-03 , DOI: 10.1002/jgt.22644
Stijn Cambie 1
Affiliation  

In 1984, Plesn\'{i}k determined the minimum total distance for given order and diameter and characterized the extremal graphs and digraphs. We prove the analog for given order and radius, when the order is sufficiently large compared to the radius. This confirms asymptotically a conjecture of Chen et al. We show the connection between minimizing the total distance and maximizing the size under the same conditions. We also prove some asymptotically optimal bounds for the maximum total distance.

中文翻译:

给定半径 I 的图的极值总距离

1984 年,Plesn\'{i}k 确定了给定阶数和直径的最小总距离,并表征了极值图和有向图。我们证明了给定阶次和半径的模拟,当阶次与半径相比足够大时。这逐渐证实了 Chen 等人的猜想。我们展示了在相同条件下最小化总距离和最大化尺寸之间的联系。我们还证明了最大总距离的一些渐近最优边界。
更新日期:2020-11-03
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