Graph Degree and Some Condition If $G$ be a Tree with degree $(5,r,s,1,1,1,1,1) $. (I wrote degree in non-increasing order). why all of this condition is True sometimes (I means on some condition)? I try to find an example that includes all following condition. any friends could help me?
1) $G$ has a vertex of degree 2.
2) $G$ has a vertex of degree 3.
3) there is two vertices in $G$ that distance between them is 3.
4) there is two vertices in $G$ that distance between them is 4.
Thanks.

Hint: The easiest way to this would be to simply draw trees that satisfy these conditions. You should be able to draw a tree that has degree sequence (5,2,2,1,1,1,1,1), which satisfies (1), (3), and (4), and another tree with degree sequence (5,3,1,1,1,1,1,1) that satisfies (2).
