Answer to Question #306178 in Algebra for chuppu

Question

Find all trees T where 75% of the vertices have degree 1 and the remaining 25% of the vertices of T have another degree(a fixed degree)

Answer 1

The sum of all the degrees 2n-2

So let n be the number of vertices and x be unknown n= 0.75+x

2( 0.75+ x) - 2= x+ ( 0.25x1)+(2x1)

1.5+2x-2=x+ 0.25+2

Collecting like terms

2x-x= 0.25+2+2-1.5

x= 2.75