论文标题
部分可观测时空混沌系统的无模型预测
A Tight Upper Bound on the Average Order of Dominating Sets of a Graph
论文作者
论文摘要
在本文中，我们研究了图中统治集的平均顺序，$ \ operatotorname {avd}（g）$。与其他平均图参数一样，极端图也是如此。 Beaton和Brown（2021）猜想，对于所有图表，$ n $的$ g $ of soldated $ n $没有隔离的顶点，$ \ permatatorname {avd}（g）\ leq 2n/3 $。最近，Erey（2021）证明了没有孤立顶点的森林的猜想。在本文中，我们证明了猜想并分类哪些图具有$ \ permatatorName {avd}（g）= 2n/3 $。我们还使用界限来证明Viping的猜想的平均版本。
In this paper we study the the average order of dominating sets in a graph, $\operatorname{avd}(G)$. Like other average graph parameters, the extremal graphs are of interest. Beaton and Brown (2021) conjectured that for all graphs $G$ of order $n$ without isolated vertices, $\operatorname{avd}(G) \leq 2n/3$. Recently, Erey (2021) proved the conjecture for forests without isolated vertices. In this paper we prove the conjecture and classify which graphs have $\operatorname{avd}(G) = 2n/3$. We also use our bounds to prove the average version of Vizing's Conjecture.
