In the same paper, Mader proved that the conjecture is true when T is a path. Diwan and Tholiya [A.A. Diwan, N.P. Tholiya, Non-separating trees in connected graphs, Discrete Math. 309 (2009) 5235-5237.] verified the conjecture when k = 1. In this paper, we will prove that Mader's conjecture is true when T is a star or double-star and k = 2.
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