Let T be a tree of order n with V (T ) = {v1, v2, . . . , vn} and deg vi = di (1 i n)
Chapter 13, Problem 24(choose chapter or problem)
Let T be a tree of order n with V (T ) = {v1, v2, . . . , vn} and deg vi = di (1 i n) such that d1 d2 dn. Prove that di _n1 i _ for each integer i. [Hint: (1) Use a proof by contradiction and (2) note that if deg v > r, where v V (T ) and r is an integer, then deg v r + 1.]
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