Let T ∆ n denote the set of trees of order n, in which the degree of each vertex is bounded by some integer ∆. Suppose that every tree in T ∆ n is equally likely. We show that the number of vertices of degree j in T ∆ n is asymptotically normal with mean (μj + o(1))n and variance (σj + o(1))n, where μj , σj are some constants. As a consequence, we give estimate to the value of the general Zagre...
