# Math Help - Graph Theory Question

1. ## Graph Theory Question

This is an interesting class but very different from calculus. I am not sure if I am grasping the concept. I have gone through the chapter three times and still not sure. Anyway here is the problem:

Suppose four teams, the Aces, the Birds, the Cats, and the Dogs, play each other once. The Aces beat all three opponents except the Birds. The Birds lost to all opponents except the Aces. The Dogs beat the Cats. Represent the results of these games with a directed graph.

Here is what I did:
Aces Cats
Birds Dogs

Starting at Cats the arrow points to the birds then the arrow goes to the Dogs and then to the Cats and from the Cats to the Aces and then to the Birds.
Does this sound correct?
I was thinking 4x3x2x1=24 possible orders, am I on the right track with the dominance order?
Thank You,
Keith

2. Hello, Keith!

Suppose four teams, the Aces, the Birds, the Cats, and the Dogs, play each other once.
The Aces beat all three opponents except the Birds.
The Birds lost to all opponents except the Aces.
The Dogs beat the Cats.
Represent the results of these games with a directed graph.

I got this graph ... using your arrangement of letters.
Code:
    A * → → → → → → → * C
↑ \           / ↑
↑   →       ←   ↑
↑     \   /     ↑
↑       X       ↑
↑     /   \     ↑
↑   ←       →   ↑
| /           \ |
B * ← ← ← ← ← ← ← * D
Sorry, I'm not familiar with "dominance order".
Coulld you define it?

3. This is what I get,