Unlabelled tree
= Unlabelled tree
A <tree> considered up to <graph isomorphism>, with <vertex> names ignored. For example, all four <labelled trees> that are <star graphs> on $\{1,2,3,4\}$ represent one <unlabelled tree>. Dividing the total in <Cayley's formula> by $n!$ does not count <unlabelled trees>: different shapes can have different numbers of distinct labellings.