The topic is the average order of a connected induced subgraph of a graph. This generalizes, to graphs in general, the average order of a subtree of a tree. In 1983, Jamison proved that the average order of a subtree, over all trees of order n, is minimized by the path $P_n$. In 2018, Kroeker, Mol, and Oellermann conjectured that $P_n$ minimizes the average order of a connected induced subgraph over all connected graphs. The main result of this paper confirms this conjecture.

中文翻译：

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图的连接顶点集的平均大小的下限

主题是图的连通诱导子图的平均阶数。这将一般的图概括为树的子树的平均顺序。1983 年，Jamison 证明了在所有n阶树中，子树的平均阶数通过路径最小化${磷}_n$. 2018 年，Kroeker、Mol 和 Oellermann 推测${磷}_n$最小化所有连通图中的连通诱导子图的平均阶数。本文的主要结果证实了这一猜想。