For odd diameters the maximizers are generalized almost seesaw spider trees with nearly equidistributed branch lengths, completing the classification for every diameter.
Tschanz,Upper bounds for Steklov eigenvalues of subgraphs of polynomial growth Cayley graphs, Ann
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Maximizing the Steklov eigenvalues on trees with a diameter constraint
For odd diameters the maximizers are generalized almost seesaw spider trees with nearly equidistributed branch lengths, completing the classification for every diameter.