Is there a tree with 7 vertices: With 5 vertices having degree 1 and 2 vertices having degree 2?

Question

Is there a tree with seven vertices:
a) With five vertices having degree 1 and two vertices having degree 2? b) With vertices having degrees 2,2,2,3,1,1,1?

So I believe the degree is the number of children vertices there are from the vertex? For a) I believe the answer is yes because I was able to draw a tree as such but for b) I believe the answer is no because I could not conceptualize a tree like this.

I may be taking the wrong definition of degree though or might be thinking about "rooted" trees only. Thank you for any help clarifying this concept and if there is a formula/ theorem for this.

Answer 1

HINT

Since every edge will connect exactly two vertices, every edge you add to a graph will increase the sum total of all degrees of all vertices in the graph by $2$. So ... the sum total should always be what kind of number?

So, count a little harder for whatever you drew for a) ...

Also, try a little harder for b) ...

Answer 2

For (b) start drawing from the vertices of degree 1, since the look of the graph at those vertices is unique.

You can probably get to this example:

.-.-.-.-.<: