For a graph G, and two distinct vertices u v of let $$ n_{{G(u,v)}} n G ( , ) be the number that are closer in to than v. Miklavi? Šparl arXiv:2011.01635v1 define distance-unbalancedness $${{\mathrm{uB}}}(G)$$ uB as sum $$|n_G(u,v)-n_G(v,u)|$$ | - over all unordered pairs G. positive integers up 15, they determine trees T fixed order with smallest largest values $${\mathrm{uB}}(T)$$ respectivel...