Abstract
AbstractThe mean subtree order of a given graph , denoted , is the average number of vertices in a subtree of . Let be a connected graph. Chin et al. conjectured that if is a proper spanning supergraph of , then . Cameron and Mol disproved this conjecture by showing that there are infinitely many pairs of graphs and with , and such that . They also conjectured that for every positive integer , there exists a pair of graphs and with , , and such that . Furthermore, they proposed that provided . In this note, we confirm these two conjectures.
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