Answer to Question #217543 in Discrete Mathematics for Ahmed Khan

Question

Q.No.5. [2+1+3]

a) Draw a tree with n vertices with n+1 vertices of degree 2, n+2 vertices of degree 3, and n+3 vertices of degree 1. Where n is even digit of your arid number e.g 19-arid-234 take n=2

Answer 1

The number of vertices of odd degree in a graph is always even (Reinhard Diestel,

"Graph Theory", p.5).

For n+2 vertices of degree 3, and n+3 vertices of degree 1:

$$n+2+n+3=2n+5 - the \space result \space is \space always \space odd$$

Answer: impossible to draw required tree