On the extrema of the mean subtree order of graphs
Abstract
It has been conjectured that the minimum and maximum of the mean subtree order among connected graphs of order n are attained by the path Pn and clique Kn, respectively. Extending ideas due to Haslegrave and Vince, we confirm that the minimum is indeed attained by Pn. On the other hand, we discuss different approaches (both promising and flawed) that could lead to a proof of the extremality of Kn.
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