论文标题
图的主导集的平均顺序
The Average Order of Dominating Sets of a Graph
论文作者
论文摘要
该论文重点介绍了图的主导集的平均顺序。我们在$ n $顶点上所有图表的最大值和最小值的最大值和最小值的最大图表中找到，而对于树，我们证明恒星可以最大程度地减少主导集的平均顺序。我们证明，没有隔离顶点的图表中主导集的平均顺序最多为$ 3N/4 $，但提供了证据表明，实际上限为$ 2N/3 $。最后，我们表明，对于几乎所有图形，我们的平均化平均水平且密度为$ [1/2,1] $，往往趋于$ \ frac {1} {2} $。
This papers focuses on the average order of dominating sets of a graph. We find the extremal graphs for the maximum and minimum value over all graphs on $n$ vertices, while for trees we prove that the star minimizes the average order of dominating sets. We prove the average order of dominating sets in graphs without isolated vertices is at most $3n/4$, but provide evidence that the actual upper bound is $2n/3$. Finally, we show that the normalized average, while dense in $[1/2,1]$, tends to $\frac{1}{2}$ for almost all graphs.
