It was conjectured by Koh and Tay [Graphs Combin. 18(4) (2002), 745–756] that for \(n\ge 5\) every simple graph of order n and size at least \(\left( {\begin{array}{c}n\\ 2\end{array}}\right) -n+5\) has an orientation of diameter two. We prove this conjecture and hence determine for every \(n\ge 5\) the minimum value of m such that every graph of order n and size m has an orientation of diameter two.

中文翻译：

---

直径两个可定向图的大小条件

它是由Koh和Tay猜想的。18（4）（2002），745–756]，对于\（n \ ge 5 \），每个阶次为n且大小至少为\（\ left（{\ begin {array} {c} n \\ 2 \ end {array}} \ right）-n + 5 \）的直径为2。我们证明了这个猜想，因此确定每个\（n \ ge 5 \）的m的最小值，使得n阶和大小为m的每个图的直径方向均为2。