On trees with algebraic connectivity greater than or equal to 2( 1-cos( π/7) )

Let T be a tree on n vertices and algebraic connectivity α (T). The trees on n≥ 45 vertices and α (T)≥5-√(21)/2 have already been completely characterized. In case of α (T)≥ 2-√(3) , it was proved that this set of trees can be partitioned in six classes, C_i, 1 ≤ i ≤ 6, ordered by algebraic connectivity, in the sense that α (T_i)>α (T_j) whenever T_i ∈ C_i, T_j ∈ C_j, and 1 ≤ i更多