# Thread: More trees ....This one is doing my head in ...

1. ## More trees ....This one is doing my head in ...

Let T be a tree on 12 vertices which has exactly 3 vertices of degree 3 and exactly onevertex of degree
2.
(a) What is the sum of the degrees of the 8 remaining vertices?
(b) What is the maximum degree of this tree? Justify your answer.
(c) What is the degree sequence of T?
(d) Find two non-isomorphic trees with this degree sequence

Ok everytime I draw a Tree it has 11 vertices only matching the first part of the problem....

(a) If I could draw the tree would I just add the remaining 8 degrees ie what ever isnt included with the 3 vertices and 3 degrees as well as the degree 2 that is on one vertex.
(b) Maximum degree ...hmmm would help if i knew what it looked like
(c) The sequence would just be the degrees ...in a sequence..
(d) so isomorphic graphs are bijective and share the same vertices being adjacent in a sequence ..therefore I'd have to draw a tree with the sequence but not bijective...

Any help would be appreciated....when I was a kid looking at my christmas tree, xmas eve hoping for some presents the next morning I never thought I'd do graph theory as an adult..just what goodies I was hoping to get...a good math brain would have been a nice present...thanks Santa ...facepalm..

2. ## Re: More trees ....This one is doing my head in ...

A tree (with at least 2 vertices) must have at least 2 vertices of degree 1. That will help.

3. ## Re: More trees ....This one is doing my head in ...

Originally Posted by bee77
Let T be a tree on 12 vertices which has exactly 3 vertices of degree 3
and exactly one vertex of degree 2.
(a) What is the sum of the degrees of the 8 remaining vertices?
(b) What is the maximum degree of this tree? Justify your answer.
(c) What is the degree sequence of T?
(d) Find two non-isomorphic trees with this degree sequence

4. ## Re: More trees ....This one is doing my head in ...

Thanks plato ,my tree looked like an arrow head ,cheers

5. ## Re: More trees ....This one is doing my head in ...

Originally Posted by bee77
Thanks plato ,my tree looked like an arrow head ,cheers