Euler Path or Euler Circuit?? Please help!

[aburchett]

[attachment=0:2ehlqjfn]image064.gif[/attachment:2ehlqjfn]Given the attached graph, list all the even vertices.

 

[tkhunny]

Is there a vertex in particular that puzzles you?

 

[aburchett]

If you could explain to me how to figure this problem out I would greatly appreciate it.

 

[Loren]

At any given vertex, count the number of paths that enter or leave that vertex. That number will be an even number or an odd number, hence, the vertex is "even" or "odd".

 

[aburchett]

So I have come up with:
Vertex Degree
A 2
B
C 3
D 3
E 2
F 2

However, I am stuck on Vertex B, would it be 3 or 4? I think I remember reading that when you have a loop you count each end of the loop when determining the degree. So would it make it 4 then?

 

[tkhunny]

We finally get back to my original question. It appears "B" is the answer. The loop has to be two or zero. It can't be one.

If it's zero, there isn't really an edge. That won't work.
If it's one, we don't actually return from our voyage along the edge. That won't do.

Not too many more choices.