论文标题
给定半径的最大图形大小
Maximum size of digraphs of given radius
论文作者
论文摘要
在$ 1967 $中，Vize确定了具有给定订单和半径的图形的最大尺寸。 $ 1973 $，弗里德曼（Fridman）回答了给定订单和Outradius的Digraphs的同样问题。我们在限制双连接的挖掘物时调查了这个问题。双连接的图形是具有有限的总距离的挖掘物，因此有趣的是，我们想注意到最小化总距离与在相同约束下最大化大小之间的联系。我们表征了极大的挖掘，以最大化订单$ n $和Outradius $ 3 $的所有双连接挖掘物以及与Outradius相比足够大的订单时。因此，我们渐近地解决了Dankelmann的问题。我们还考虑了这些问题，用于两分的挖掘物，并部分解决了Dankelmann的第二个问题。
In $1967$, Vizing determined the maximum size of a graph with given order and radius. In $1973$, Fridman answered the same question for digraphs with given order and outradius. We investigate that question when restricting to biconnected digraphs. Biconnected digraphs are the digraphs with a finite total distance and hence the interesting ones, as we want to note a connection between minimizing the total distance and maximizing the size under the same constraints. We characterize the extremal digraphs maximizing the size among all biconnected digraphs of order $n$ and outradius $3$, as well as when the order is sufficiently large compared to the outradius. As such, we solve a problem of Dankelmann asymptotically. We also consider these questions for bipartite digraphs and solve a second problem of Dankelmann partially.
