Maximum average subtree order among graphs

Determine the maximum average subtree order among graphs of a fixed order.

Background

The paper studies the analogous extremal problem for the average length of subpaths and proves that the complete graph maximizes this quantity among graphs of a given order. In contrast, the corresponding problem for the average subtree order remains unresolved, as noted in comparison with the subpath setting.

References

Also the analogue of determining the maximum among graphs is resolved, $ \avp(G) \le \avp(K_n)$, while it is open for the average subtree order.

— The number and average length of subpaths in graphs  (2608.23542 - Cambie, 24 Aug 2026) in Section 1, Introduction