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Mar 12 at 5:28 comment added Fedor Petrov @bof ah, a graded tree with every vertex on the $n$-the level having $n$ children
Mar 12 at 2:45 comment added bof Concretely, let the vertices be finite sequences $(a_1,a_2,\dots,a_n)$ with $a_i\in\{1,2,\dots,i\}$ and make $(a_1,\dots,a_n)$ adjacent to $(a_1,\dots,a_n,a_{n+1})$.
Mar 8 at 21:02 comment added Dominic van der Zypen Quite remarkable that all vertices can be shy, thanks for this example!
Mar 8 at 8:57 vote accept Dominic van der Zypen
Mar 8 at 7:49 history answered Fedor Petrov CC BY-SA 4.0