Combinatorics and Graph Theory · Problem 5.5.8

Graph Theory — David Guichard

Mathematics — Combinatorics · trees

Problem

Suppose

T

is a tree on

n

vertices,

k

of which have degree larger than 1,

d_1, d_2, \ldots, d_k

. Of course,

T

must also have pendant vertices. How many pendant vertices? Your answer should depend only on

k

and

d_1, d_2, \ldots, d_k